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Aage 20 Oct 2017, 08:54
I am seraching a solution of:
c1*y^2+c2+dy/dx = 0
c1 and c2 are constants
1. Solving Differential Equations
Different math books, have not been able to find a solution.
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I am seraching a solution of: c1*y^2+c2+dy/dx = 0 c1 and c2 are constants
Relevant page <a href="https://www.intmath.com/differential-equations/1-solving-des.php">1. Solving Differential Equations</a> What I've done so far Different math books, have not been able to find a solution.
Murray 20 Oct 2017, 23:03
@Aage: This is actually a non-linear differential equation, which is beyond the scope of the IntMath Forum. This PDF has a similar example which you may find useful: An Example of a Non-linear Differential Equation
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@Aage: This is actually a <b>non-</b>linear differential equation, which is beyond the scope of the IntMath Forum. This PDF has a similar example which you may find useful: <a href="https://math.dartmouth.edu/archive/m23s06/publichtml/handouts/nonlinearexample.pdf">An Example of a Non-linear Differential Equation</a>
stephenB 14 Oct 2019, 07:06
You should not dismiss the problem as nonlinear before trying the frobenius method, revealing the solution y = (c2/c1)/x. This means there exists some transformation to a linear system, provided the singular point is removed.
Alternatively, you can solve this problem simply by deducing the proper transform: z=1/y.
The resulting ode factors:
(1/z^2)(1-c2/c1*dz/dx) =0.
So for y not zero, the solution (above) exists linearly.
Thanks for your website.
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You should not dismiss the problem as nonlinear before trying the frobenius method, revealing the solution y = (c2/c1)/x. This means there exists some transformation to a linear system, provided the singular point is removed. Alternatively, you can solve this problem simply by deducing the proper transform: z=1/y. The resulting ode factors: (1/z^2)(1-c2/c1*dz/dx) =0. So for y not zero, the solution (above) exists linearly. Thanks for your website.
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@stephenB: Thanks for your input.
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