What is the solution for y^{''}-5y^'=10x+3 ?

The solution for y^{''}-5y^'=10x+3 is y=c_{1}e^{5x}+c_{2}-x^2-x

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y^{''}-5y^'=10x+3

y^{^{''}} - 5 y^{^{'}} = 10 x + 3

y = c_{1} e^{5 x} + c_{2} - x^{2} - x

Solution steps

y^{''} (x) - 5 y^{'} (x) = 10 x + 3

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} - x^{2} - x

y = c_{1} e^{5 x} + c_{2} - x^{2} - x

x y y^{^{'}} + x^{2} + y^{2} = 0

\int \frac{5 x ^{4} + 6}{x ^{5} + 6 x} d x

x \to 5 + lim (\frac{4}{x - 5})

x \to 0 lim (x^{8} - \frac{1}{x})

\frac{d}{d x} (sin^{3} (2 x) - cos (2 x))

What is the solution for y^{''}-5y^'=10x+3 ?
The solution for y^{''}-5y^'=10x+3 is y=c_{1}e^{5x}+c_{2}-x^2-x