What is the solution for (d^2y)/(dx^2)+2(dy)/(dx)+2y=2(x+1)^2 ?

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

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 2 (x + 1)^{2}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 2 y = 2 (x + 1)^{2}

Solve linear ODE:

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

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

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

y^{^{''}} - 2 y^{^{'}} + 5 y = 8, y (0) = 2, y^{^{'}} (0) = 2

y^{^{''}} - 2 y^{^{'}} + y = 3 e^{2 x} - 5 e^{4 x}

y^{^{''}} + y = 2 cos (3 x)

y^{^{''}} - 7 y^{^{'}} + 12 y = e^{4 x}

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