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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 6 y^{^{'}} + 9 y = 16 e^{7} t, y (0) = 7, y^{^{'}} (0) = 4

y^{^{''}} + 6 y + 34 = 0, y (0) = 3

y^{^{''}} + 2 y^{^{'}} - 3 y = 3 e^{2 t}

y^{^{''}} - 3 y^{^{'}} = 2 x - 2

y^{^{''}} + 4 y^{^{'}} + 5 y = - 15 x + e - x

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