What is the solution for (d^2+2d+10)y=25x^2+3 ?

The solution for (d^2+2d+10)y=25x^2+3 is y=e^{-x}(c_{1}cos(3x)+c_{2}sin(3x))+(5x^2)/2-x

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(d^2+2d+10)y=25x^2+3

(d^{2} + 2 d + 10) y = 25 x^{2} + 3

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 x ^{2}}{2} - x

Solution steps

(d^{2} + 2 d + 10) y = 25 x^{2} + 3

Solve linear ODE:

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 x ^{2}}{2} - x

y = e^{- x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{5 x ^{2}}{2} - x

(d^{2} + 4 d) y = 12

(d^{2} + 4) \cdot y = x^{2}

(d^{2} - d - 2) y = 2 lo g_{10} (x) + \frac{1}{x} + \frac{1}{x ^{2}}

y^{^{''}} - y = x^{2} \cdot e^{x} + 5

y^{^{''}} + 5 y^{^{'}} + 6 y = 5 sin (x)

What is the solution for (d^2+2d+10)y=25x^2+3 ?
The solution for (d^2+2d+10)y=25x^2+3 is y=e^{-x}(c_{1}cos(3x)+c_{2}sin(3x))+(5x^2)/2-x