What is the solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 ?

The solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 is y=4e^{2t}-7e^t+4e^{2t}t

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5

y^{^{''}} - 3 y^{^{'}} + 2 y = 4 e^{2 t}, y (0) = - 3, y^{^{'}} (0) = 5

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

Solution steps

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

Solve linear ODE:

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

y = 4 e^{2 t} - 7 e^{t} + 4 e^{2 t} t

y^{^{''}} + y^{^{'}} + 2 y - x - 3 = 0, y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 4 y = e^{t}

x^{^{''}} + 4 x^{^{'}} + 4 x = 4 t^{2} + 6 e^{t}

y^{^{''}} - y = 2 x^{2} - x - 3

\frac{d ^{2} y}{d x ^{2}} - 16 \frac{d y}{d x} + 16 y = 16 (x - 1)

What is the solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 ?
The solution for y^{''}-3y^'+2y=4e^{2t},y(0)=-3,y^'(0)=5 is y=4e^{2t}-7e^t+4e^{2t}t