What is the solution for (d^2y)/(dx^2)+2y=6x,y(0)=0,y^'(0)=0 ?

The solution for (d^2y)/(dx^2)+2y=6x,y(0)=0,y^'(0)=0 is y=3x-3/(sqrt(2))sin(sqrt(2)x)

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(d^2y)/(dx^2)+2y=6x,y(0)=0,y^'(0)=0

\frac{d ^{2} y}{d x ^{2}} + 2 y = 6 x, y (0) = 0, y^{^{'}} (0) = 0

y = 3 x - \frac{3}{2} sin (2 x)

Solution steps

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

Solve linear ODE:

y = 3 x - \frac{3}{2} sin (2 x)

y = 3 x - \frac{3}{2} sin (2 x)

y^{^{''}} (p) + 6 y^{^{'}} (p) + 9 y (p) = p

y^{^{''}} - 2 y^{^{'}} - 35 y = 768 e^{- t}

y^{^{''}} - y^{^{'}} - 6 y = - e^{x} + 12

y^{^{''}} + 4 y = sec (22 x)

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

What is the solution for (d^2y)/(dx^2)+2y=6x,y(0)=0,y^'(0)=0 ?
The solution for (d^2y)/(dx^2)+2y=6x,y(0)=0,y^'(0)=0 is y=3x-3/(sqrt(2))sin(sqrt(2)x)