Finding Orthogonal Trajectories of $frac{x^2}{a}-frac{y^2}{a-1}=1$
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Find Orthogonal Trajectories of $frac{x^2}{a}-frac{y^2}{a-1}=1$
Hint. Substitute
$x^2=w$
$y^2=z$
My attempt
substituting $x$ and $y$ i get
$$frac{w}{a}-frac{z}{a-1}=1quad /a(a-1)$$
$$w(a-1)-za=a(a-1)quad /'$$
$$w'(a-1)-z'a=0$$
I got so far but i'm not sure how to go on from here can somebody help me find out $w'$and $z'$ and help me finish the problem
differential-equations
asked Nov 21 at 11:03
westlife
718
add a comment |
up vote
0
down vote
favorite
Find Orthogonal Trajectories of $frac{x^2}{a}-frac{y^2}{a-1}=1$
Hint. Substitute
$x^2=w$
$y^2=z$
My attempt
substituting $x$ and $y$ i get
$$frac{w}{a}-frac{z}{a-1}=1quad /a(a-1)$$
$$w(a-1)-za=a(a-1)quad /'$$
$$w'(a-1)-z'a=0$$
I got so far but i'm not sure how to go on from here can somebody help me find out $w'$and $z'$ and help me finish the problem
differential-equations
asked Nov 21 at 11:03
westlife
718
Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
Find Orthogonal Trajectories of $frac{x^2}{a}-frac{y^2}{a-1}=1$
Hint. Substitute
$x^2=w$
$y^2=z$
My attempt
substituting $x$ and $y$ i get
$$frac{w}{a}-frac{z}{a-1}=1quad /a(a-1)$$
$$w(a-1)-za=a(a-1)quad /'$$
$$w'(a-1)-z'a=0$$
I got so far but i'm not sure how to go on from here can somebody help me find out $w'$and $z'$ and help me finish the problem
differential-equations
asked Nov 21 at 11:03
westlife
718
Find Orthogonal Trajectories of $frac{x^2}{a}-frac{y^2}{a-1}=1$
Hint. Substitute
$x^2=w$
$y^2=z$
My attempt
substituting $x$ and $y$ i get
$$frac{w}{a}-frac{z}{a-1}=1quad /a(a-1)$$
$$w(a-1)-za=a(a-1)quad /'$$
$$w'(a-1)-z'a=0$$
I got so far but i'm not sure how to go on from here can somebody help me find out $w'$and $z'$ and help me finish the problem
differential-equations
differential-equations
asked Nov 21 at 11:03
westlife
718
asked Nov 21 at 11:03
westlife
718
asked Nov 21 at 11:03
westlife
718
asked Nov 21 at 11:03
westlife
718
asked Nov 21 at 11:03
westlife
718
718
Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07
add a comment |
Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07
Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07
Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07
add a comment |
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Could you please explain what you are doing ?
– Yves Daoust
Nov 21 at 11:07