What is the solution for (d^2y)/(dx^2)+y=4x ?

The solution for (d^2y)/(dx^2)+y=4x is y=c_{1}cos(x)+c_{2}sin(x)+4x

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(d^2y)/(dx^2)+y=4x

\frac{d ^{2} y}{d x ^{2}} + y = 4 x

y = c_{1} cos (x) + c_{2} sin (x) + 4 x

Solution steps

\frac{d ^{2} y}{d x ^{2}} + y = 4 x

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 4 x

y = c_{1} cos (x) + c_{2} sin (x) + 4 x

y^{^{''}} + 5 y^{^{'}} + 6 y = 1 + e^{- t}

y^{^{''}} + 2 y^{^{'}} - 8 = 0

0.5 q^{^{''}} + 20 q^{^{'}} + \frac{1}{0.0025} q = 100

x^{^{''}} + 16 x = 14 cos (3 t)

y^{^{''}} - 2 y^{^{'}} + y = t \cdot e^{t}

What is the solution for (d^2y)/(dx^2)+y=4x ?
The solution for (d^2y)/(dx^2)+y=4x is y=c_{1}cos(x)+c_{2}sin(x)+4x