u_(xx)+y^2u= sin2x I want to solve the non homogeneous differential equation (del^2 u)/( del x^2}+y^2u= sin 2x.

Chelsea Pruitt 2022-10-25 Answered
u x x + y 2 u = sin 2 x
I want to solve the non homogeneous differential equation
2 u x 2 + y 2 u = sin 2 x .
I have tried to solve it by method of separable of variables. But unfortunately, not able to find out the solution. Please give me some hints to solve it.
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Answers (1)

lipovicai1w
Answered 2022-10-26 Author has 9 answers
Use the method of undetermined characteristics and the methods from ODE's. u = v + w where v solves v x x + y 2 v = 0 and w = A ( y ) sin ( 2 x ) + B ( y ) cos ( 2 x )
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