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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

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

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x}{2} + \frac{1}{2}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x}{2} + \frac{1}{2}

y = c_{1} e^{2 x} + c_{2} x e^{2 x} + \frac{x}{2} + \frac{1}{2}

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