What is the solution for x^2y^{''}+xy^'+9y=10x ?

The solution for x^2y^{''}+xy^'+9y=10x is y=c_{1}cos(3ln(x))+c_{2}sin(3ln(x))+x

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x^2y^{''}+xy^'+9y=10x

x^{2} y^{^{''}} + x y^{^{'}} + 9 y = 10 x

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)) + x

Solution steps

x^{2} y^{''} (x) + x y^{'} (x) + 9 y = 10 x

Solve linear ODE:

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)) + x

y = c_{1} cos (3 ln (x)) + c_{2} sin (3 ln (x)) + x

y = x^{3} + 2

\int tan^{3} (6 x) d x

\int \frac{x}{x ^{2} - 6 x + 5} d x

\int (7 + x - 3 x^{2}) e^{- x} d x

sin (x)

What is the solution for x^2y^{''}+xy^'+9y=10x ?
The solution for x^2y^{''}+xy^'+9y=10x is y=c_{1}cos(3ln(x))+c_{2}sin(3ln(x))+x