What is the solution for y^{''}+y=xe^x+sin(2x) ?

The solution for y^{''}+y=xe^x+sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)+(e^xx)/2-1/2 e^x-1/3 sin(2x)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}+y=xe^x+sin(2x)

y^{^{''}} + y = x e^{x} + sin (2 x)

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

Solution steps

y^{''} (x) + y = x e^{x} + sin (2 x)

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} - 12 y = x e^{2 x}

x^{^{''}} - 2 x^{^{'}} - x = e^{2 t}

y^{^{''}} + 25 y = e^{- t}

y^{^{''}} - y = e^{x} cos (x), y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - 6 y = e^{x}

What is the solution for y^{''}+y=xe^x+sin(2x) ?
The solution for y^{''}+y=xe^x+sin(2x) is y=c_{1}cos(x)+c_{2}sin(x)+(e^xx)/2-1/2 e^x-1/3 sin(2x)