What is the solution for y^{''}-8y^'+20y=100x^2 ?

The solution for y^{''}-8y^'+20y=100x^2 is y=e^{4x}(c_{1}cos(2x)+c_{2}sin(2x))+5x^2+4x+11/10

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y^{''}-8y^'+20y=100x^2

y^{^{''}} - 8 y^{^{'}} + 20 y = 100 x^{2}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10}

Solution steps

y^{''} (x) - 8 y^{'} (x) + 20 y = 100 x^{2}

Solve linear ODE:

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10}

y = e^{4 x} (c_{1} cos (2 x) + c_{2} sin (2 x)) + 5 x^{2} + 4 x + \frac{11}{10}

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

y^{^{''}} - 8 y^{^{'}} + 16 y = \frac{e ^{4 x}}{x}

(2 D^{2} - 3 D + 1) y = csc (2 π x)

d, d (x) = \frac{x ^{2} + 13 x + 42}{x ^{2} - 3 x - 28}

y^{^{''}} - 7 y^{^{'}} = x^{2}

What is the solution for y^{''}-8y^'+20y=100x^2 ?
The solution for y^{''}-8y^'+20y=100x^2 is y=e^{4x}(c_{1}cos(2x)+c_{2}sin(2x))+5x^2+4x+11/10