What is the solution for y^{''}-2y^'+5y=5x+3 ?

The solution for y^{''}-2y^'+5y=5x+3 is y=e^x(c_{1}cos(2x)+c_{2}sin(2x))+x+1

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y^{''}-2y^'+5y=5x+3

y^{^{''}} - 2 y^{^{'}} + 5 y = 5 x + 3

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x + 1

Solution steps

y^{''} (x) - 2 y^{'} (x) + 5 y = 5 x + 3

Solve linear ODE:

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x + 1

y = e^{x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + x + 1

x \to 3 lim (\frac{3 - x}{∣ x - 3 ∣})

\int (8 x + 1 - 9 e^{x}) d x

\frac{e ^{- s}}{s ^{2} + 3 s + 2}

\int \frac{e ^{- x}}{( 9 e ^{- 2 x} + 1 ) ^{\frac{3}{2}}} d x

1 - x^{2}

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