en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

y^{''}+y^'+y=sinh(x)

Solution

y^{^{''}} + y^{^{'}} + y = sinh (x)

Solution

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

Solution steps

y^{''} (x) + y^{'} (x) + y = sinh (x)

Solve linear ODE:

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

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

Popular Examples

(d^2y)/(dt^2)-4y=tcos(2t),y=0,t=0

y^{''}+25y=20sec(5t)

y^{''}-1y=tan(x)

y^{'''}+y^{''}-4=0

y^{''}-8y^'-4y-2=2x

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y^'+y=sinh(x) ?
The solution for y^{''}+y^'+y=sinh(x) is