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

The solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=4x^2 is y=c_{1}e^{-x}+c_{2}e^{-2x}+2x^2-6x+7

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 2 x^{2} - 6 x + 7

Solution steps

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

Solve linear ODE:

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 2 x^{2} - 6 x + 7

y = c_{1} e^{- x} + c_{2} e^{- 2 x} + 2 x^{2} - 6 x + 7

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{2 x}

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

x^{^{''}} + 3 x^{^{'}} + 2 x = sin (t)

y^{^{''}} + 4 y = 2 sec (2 t)

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

What is the solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=4x^2 ?
The solution for (d^2y)/(dx^2)+3(dy)/(dx)+2y=4x^2 is y=c_{1}e^{-x}+c_{2}e^{-2x}+2x^2-6x+7