What is the solution for (d^2y)/(dx^2)+4y=-3x^2+2x+3 ?

The solution for (d^2y)/(dx^2)+4y=-3x^2+2x+3 is y=c_{1}cos(2x)+c_{2}sin(2x)-(3x^2)/4+x/2+9/8

Popular >

(d^2y)/(dx^2)+4y=-3x^2+2x+3

\frac{d ^{2} y}{d x ^{2}} + 4 y = - 3 x^{2} + 2 x + 3

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{3 x ^{2}}{4} + \frac{x}{2} + \frac{9}{8}

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 4 y = - 3 x^{2} + 2 x + 3

Solve linear ODE:

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{3 x ^{2}}{4} + \frac{x}{2} + \frac{9}{8}

y = c_{1} cos (2 x) + c_{2} sin (2 x) - \frac{3 x ^{2}}{4} + \frac{x}{2} + \frac{9}{8}

y^{^{''}} + 16 y = g (t), y (0) = 5, y^{^{'}} (0) = 0

y^{^{''}} - 6 y^{^{'}} + 9 y = e^{3 t} ln (t)

y^{^{''}} - y^{^{'}} - 2 y = 1, y (0) = 1, y^{^{'}} (0) = 3

\frac{d ^{2} y}{d x ^{2}} - 9 \frac{d y}{d x} + 6 y = x e^{x}

(D^{2} - 4 D + 4) y = e^{- 4 x} + 5 cos (3 x)

What is the solution for (d^2y)/(dx^2)+4y=-3x^2+2x+3 ?
The solution for (d^2y)/(dx^2)+4y=-3x^2+2x+3 is y=c_{1}cos(2x)+c_{2}sin(2x)-(3x^2)/4+x/2+9/8