What is the solution for y^{''}+6y=-294x^2e^6x ?

The solution for y^{''}+6y=-294x^2e^6x is y=c_{1}cos(sqrt(6)x)+c_{2}sin(sqrt(6)x)-49e^6x^3+49e^6x

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y^{''}+6y=-294x^2e^6x

y^{^{''}} + 6 y = - 294 x^{2} e^{6} x

y = c_{1} cos (6 x) + c_{2} sin (6 x) - 49 e^{6} x^{3} + 49 e^{6} x

Solution steps

y^{''} (x) + 6 y = - 294 x^{2} e^{6} x

Solve linear ODE:

y = c_{1} cos (6 x) + c_{2} sin (6 x) - 49 e^{6} x^{3} + 49 e^{6} x

y = c_{1} cos (6 x) + c_{2} sin (6 x) - 49 e^{6} x^{3} + 49 e^{6} x

y^{^{''}} + 4 y^{^{'}} + 3 y = e^{- 3 x}

y^{^{''}} - y^{^{'}} - 2 y = 1

v^{^{''}} - 16 v = 2 e^{4 x}

y^{^{''}} + 2 y^{^{'}} + y = t^{5} e^{- t}

y^{^{''}} + 49 y = 17 sec^{2} (7 t)

What is the solution for y^{''}+6y=-294x^2e^6x ?
The solution for y^{''}+6y=-294x^2e^6x is y=c_{1}cos(sqrt(6)x)+c_{2}sin(sqrt(6)x)-49e^6x^3+49e^6x