What is the solution for (d^2y)/(dx^2)+6(dy)/(dx)+10y=50x ?

The solution for (d^2y)/(dx^2)+6(dy)/(dx)+10y=50x is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+5x-3

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(d^2y)/(dx^2)+6(dy)/(dx)+10y=50x

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 10 y = 50 x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 6 \frac{d y}{d x} + 10 y = 50 x

Solve linear ODE:

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

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

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

y^{^{''}} + 8 y^{^{'}} + 16 y = 4 e^{- 4 t}

y^{^{''}} - 3 y^{^{'}} + 2 y = 3 cos (3 t), y (0) = 2, y^{^{'}} (0) = 3

x^{^{''}} + x = sin (2 t)

y^{^{''}} + 16 y = 11 sec^{2} (4 t)

What is the solution for (d^2y)/(dx^2)+6(dy)/(dx)+10y=50x ?
The solution for (d^2y)/(dx^2)+6(dy)/(dx)+10y=50x is y=e^{-3x}(c_{1}cos(x)+c_{2}sin(x))+5x-3