What is the solution for (D^4-1)y=7x^2 ?

The solution for (D^4-1)y=7x^2 is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)-7x^2

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(D^4-1)y=7x^2

(D^{4} - 1) y = 7 x^{2}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

Solution steps

(D^{4} - 1) y = 7 x^{2}

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

y = c_{1} e^{x} + c_{2} e^{- x} + c_{3} cos (x) + c_{4} sin (x) - 7 x^{2}

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{5 x}

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{- 4 t}, y (0) = 1

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

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

\frac{d ^{2} y}{d x ^{2}} + 5 \frac{d y}{d x} + 6 = 0

What is the solution for (D^4-1)y=7x^2 ?
The solution for (D^4-1)y=7x^2 is y=c_{1}e^x+c_{2}e^{-x}+c_{3}cos(x)+c_{4}sin(x)-7x^2