What is the solution for y^{''}-8y^'+16y=0,y(0)=-4,y^'(0)=-71/5 ?

The solution for y^{''}-8y^'+16y=0,y(0)=-4,y^'(0)=-71/5 is y=-4e^{4t}+(9e^{4t}t)/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-8y^'+16y=0,y(0)=-4,y^'(0)=-71/5

y^{^{''}} - 8 y^{^{'}} + 16 y = 0, y (0) = - 4, y^{^{'}} (0) = - \frac{71}{5}

y = - 4 e^{4 t} + \frac{9 e ^{4 t} t}{5}

Solution steps

y^{''} (t) - 8 y^{'} (t) + 16 y = 0

Solve linear ODE:

y = - 4 e^{4 t} + \frac{9 e ^{4 t} t}{5}

y = - 4 e^{4 t} + \frac{9 e ^{4 t} t}{5}

25 y^{^{''}} + 10 y^{^{'}} + 1 y = 0

3 y^{^{''}} - 13 y^{^{'}} + 14 y = 0

2 y^{^{''}} + 13 y^{^{'}} - 7 y = 0

10 x^{^{''}} + 7 x^{^{'}} + x = 0

y^{^{''}} + 8 y^{^{'}} + 16 y = 0, y (- 1) = 3, y^{^{'}} (- 1) = 5

What is the solution for y^{''}-8y^'+16y=0,y(0)=-4,y^'(0)=-71/5 ?
The solution for y^{''}-8y^'+16y=0,y(0)=-4,y^'(0)=-71/5 is y=-4e^{4t}+(9e^{4t}t)/5