Non linear second order diff eq

Thread starter rbetzel
Start date Feb 3, 2009
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Diff eq Linear Second order

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SUMMARY

The discussion focuses on solving the non-linear second-order differential equation defined as y'' + a(y')^2 - by = 0. A proposed substitution involves differentiating the equation to obtain y''' + 2ay'y'' - b = 0. Additionally, the substitution u = y' transforms the equation into u'' + 2au'u - b = 0, which simplifies the analysis of the original equation.

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Understanding of second-order differential equations
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Knowledge of substitution methods in differential equations
Basic calculus, particularly differentiation

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Feb 3, 2009

rbetzel

I'm trying to find a substitution that works for the nonlin diffeq

y''+a(y')^2-by=0

Any suggestions?

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Feb 3, 2009

NoMoreExams

If you differentiate again, you get

[tex]y^{'''} + 2ay^{'} \cdot y^{''} - b = 0[/tex] right?

If you let

[tex]u = y^{'}[/tex] you get [tex]u^{''} + 2a u^{'}u - b = 0[/tex]