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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 4 y = 4 sin (2 x) - 3 e^{2} x

Solve linear ODE:

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

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

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