Does a differential equation with no solution mean the function is just zero?
Does a differential equation with no solution mean the function is just zero? I am trying to solve a non-linear ODE and the solution will then be plugged into another equation, and having the equations solution be zero would mean:
$$A(t)=0$$
for the following equation:
$$A''(t)left(B(t)−frac{A(t)}{C(t)}right) - A(t)D(t)=0$$
not asking for a solution, but would this be the case?
differential-equations nonlinear-system
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
add a comment |
Does a differential equation with no solution mean the function is just zero? I am trying to solve a non-linear ODE and the solution will then be plugged into another equation, and having the equations solution be zero would mean:
$$A(t)=0$$
for the following equation:
$$A''(t)left(B(t)−frac{A(t)}{C(t)}right) - A(t)D(t)=0$$
not asking for a solution, but would this be the case?
differential-equations nonlinear-system
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08
add a comment |
Does a differential equation with no solution mean the function is just zero? I am trying to solve a non-linear ODE and the solution will then be plugged into another equation, and having the equations solution be zero would mean:
$$A(t)=0$$
for the following equation:
$$A''(t)left(B(t)−frac{A(t)}{C(t)}right) - A(t)D(t)=0$$
not asking for a solution, but would this be the case?
differential-equations nonlinear-system
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
Does a differential equation with no solution mean the function is just zero? I am trying to solve a non-linear ODE and the solution will then be plugged into another equation, and having the equations solution be zero would mean:
$$A(t)=0$$
for the following equation:
$$A''(t)left(B(t)−frac{A(t)}{C(t)}right) - A(t)D(t)=0$$
not asking for a solution, but would this be the case?
differential-equations nonlinear-system
differential-equations nonlinear-system
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
edited Dec 1 '18 at 22:01
mrtaurho
3,72121133
3,72121133
asked Dec 1 '18 at 22:00
bguner
11
asked Dec 1 '18 at 22:00
bguner
11
asked Dec 1 '18 at 22:00
bguner
11
11
If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08
add a comment |
If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08
If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08
add a comment |
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If a DE has no solution, that means no function can be a solution, even the zero function (there is nothing special with it, it's just a function). On the other hand, the equation you give has obviously at least one solution: the zero function.
– Jean-Claude Arbaut
Dec 1 '18 at 22:47
The zero function is a trivial solution. "no non-trivial solution" may mean zero is the only solution, but not always.
– Dylan
Dec 2 '18 at 6:08