What is the solution for y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7 ?

The solution for y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7 is y=(2-1/2)e^{3t}+1/2 e^t+2te^{3t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 t}, y (0) = 2, y^{^{'}} (0) = 7

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

Solution steps

y^{''} (t) - 4 y^{'} (t) + 3 y = 4 e^{3 t}

Solve linear ODE:

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

y = (2 - \frac{1}{2}) e^{3 t} + \frac{1}{2} e^{t} + 2 t e^{3 t}

\frac{1}{8} y^{^{''}} + 4 y^{^{'}} + 28 x = 0, y (0) = 0, y^{^{'}} (0) = 3

- 6 y^{^{''}} - 5 y^{^{'}} - y = - (t^{2} + 2 t + 2 e^{2 t})

0.75 y^{^{''}} + 50 y = 5 t^{2}

(D^{2} - 5 D + 6) y = x^{2} e^{3 x}

y^{^{''}} + 10 y^{^{'}} + 20 y = 50 sinh (5 x)

What is the solution for y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7 ?
The solution for y^{''}-4y^'+3y=4e^{3t},y(0)=2,y^'(0)=7 is y=(2-1/2)e^{3t}+1/2 e^t+2te^{3t}