Solving an Unwieldy Differential Equation
$begingroup$
I am at the end of a very long math problem and am left with this equation.
I know. It's monstrous.
This equation is equal to $frac{dtheta}{dt}$, and I would like to solve it as a differential equation. The only way I've found that might work is the separation of variables strategy:
$$frac{dtheta}{dt}=f(t)g(theta)$$
$$frac{1}{g(theta)}dtheta=f(t)dt$$
$$intfrac{1}{g(theta)}dtheta=int f(t)dt$$
$$G(theta)+c_1=F(t)+c_2$$
$$G(theta)-F(t)=C$$
The issue is that teasing apart the variables in this equation seems like it will take a very, very long time, not to mention taking the integral of what is left. It feels like this is the wrong way to do it.
So, my question is this: how do I solve this differential equation?
Thank you for all the help you can give.
calculus differential-equations
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
$endgroup$
add a comment |
$begingroup$
I am at the end of a very long math problem and am left with this equation.
I know. It's monstrous.
This equation is equal to $frac{dtheta}{dt}$, and I would like to solve it as a differential equation. The only way I've found that might work is the separation of variables strategy:
$$frac{dtheta}{dt}=f(t)g(theta)$$
$$frac{1}{g(theta)}dtheta=f(t)dt$$
$$intfrac{1}{g(theta)}dtheta=int f(t)dt$$
$$G(theta)+c_1=F(t)+c_2$$
$$G(theta)-F(t)=C$$
The issue is that teasing apart the variables in this equation seems like it will take a very, very long time, not to mention taking the integral of what is left. It feels like this is the wrong way to do it.
So, my question is this: how do I solve this differential equation?
Thank you for all the help you can give.
calculus differential-equations
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
$endgroup$
add a comment |
$begingroup$
I am at the end of a very long math problem and am left with this equation.
I know. It's monstrous.
This equation is equal to $frac{dtheta}{dt}$, and I would like to solve it as a differential equation. The only way I've found that might work is the separation of variables strategy:
$$frac{dtheta}{dt}=f(t)g(theta)$$
$$frac{1}{g(theta)}dtheta=f(t)dt$$
$$intfrac{1}{g(theta)}dtheta=int f(t)dt$$
$$G(theta)+c_1=F(t)+c_2$$
$$G(theta)-F(t)=C$$
The issue is that teasing apart the variables in this equation seems like it will take a very, very long time, not to mention taking the integral of what is left. It feels like this is the wrong way to do it.
So, my question is this: how do I solve this differential equation?
Thank you for all the help you can give.
calculus differential-equations
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
$endgroup$
I am at the end of a very long math problem and am left with this equation.
I know. It's monstrous.
This equation is equal to $frac{dtheta}{dt}$, and I would like to solve it as a differential equation. The only way I've found that might work is the separation of variables strategy:
$$frac{dtheta}{dt}=f(t)g(theta)$$
$$frac{1}{g(theta)}dtheta=f(t)dt$$
$$intfrac{1}{g(theta)}dtheta=int f(t)dt$$
$$G(theta)+c_1=F(t)+c_2$$
$$G(theta)-F(t)=C$$
The issue is that teasing apart the variables in this equation seems like it will take a very, very long time, not to mention taking the integral of what is left. It feels like this is the wrong way to do it.
So, my question is this: how do I solve this differential equation?
Thank you for all the help you can give.
calculus differential-equations
calculus differential-equations
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
asked Dec 4 '18 at 16:27
Levi BuckwalterLevi Buckwalter
1
1
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
HINT
For starters, simplify the denominator noting that
$$
l^2 sin^2 theta + l^2 cos^2 theta = l^2,
$$
and cancel one of the $l$ factor with the numerator. Finally, I would try to simplify the massive trig function on the RHS using various trig summation of sines and cosines to compact it down.
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
$endgroup$
add a comment |
Your Answer
StackExchange.ifUsing("editor", function () {
return StackExchange.using("mathjaxEditing", function () {
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
});
});
}, "mathjax-editing");
StackExchange.ready(function() {
var channelOptions = {
tags: "".split(" "),
id: "69"
};
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function() {
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled) {
StackExchange.using("snippets", function() {
createEditor();
});
}
else {
createEditor();
}
});
function createEditor() {
StackExchange.prepareEditor({
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader: {
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
},
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
});
}
});
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025784%2fsolving-an-unwieldy-differential-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
HINT
For starters, simplify the denominator noting that
$$
l^2 sin^2 theta + l^2 cos^2 theta = l^2,
$$
and cancel one of the $l$ factor with the numerator. Finally, I would try to simplify the massive trig function on the RHS using various trig summation of sines and cosines to compact it down.
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
$endgroup$
add a comment |
$begingroup$
HINT
For starters, simplify the denominator noting that
$$
l^2 sin^2 theta + l^2 cos^2 theta = l^2,
$$
and cancel one of the $l$ factor with the numerator. Finally, I would try to simplify the massive trig function on the RHS using various trig summation of sines and cosines to compact it down.
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
$endgroup$
add a comment |
$begingroup$
HINT
For starters, simplify the denominator noting that
$$
l^2 sin^2 theta + l^2 cos^2 theta = l^2,
$$
and cancel one of the $l$ factor with the numerator. Finally, I would try to simplify the massive trig function on the RHS using various trig summation of sines and cosines to compact it down.
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
$endgroup$
HINT
For starters, simplify the denominator noting that
$$
l^2 sin^2 theta + l^2 cos^2 theta = l^2,
$$
and cancel one of the $l$ factor with the numerator. Finally, I would try to simplify the massive trig function on the RHS using various trig summation of sines and cosines to compact it down.
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
answered Dec 4 '18 at 16:35
gt6989bgt6989b
33.3k22452
33.3k22452
add a comment |
add a comment |
Thanks for contributing an answer to Mathematics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function () {
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3025784%2fsolving-an-unwieldy-differential-equation%23new-answer', 'question_page');
}
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function () {
StackExchange.helpers.onClickDraftSave('#login-link');
});
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
