What is the solution for 6f^{''}(t)=3f^{''}(t)-5f(t) ?

The solution for 6f^{''}(t)=3f^{''}(t)-5f(t) is f(t)=c_{1}cos(sqrt(5/3)t)+c_{2}sin(sqrt(5/3)t)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6f^{''}(t)=3f^{''}(t)-5f(t)

6 f^{^{''}} (t) = 3 f^{^{''}} (t) - 5 f (t)

f (t) = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

Solution steps

6 f^{''} (t) = 3 f^{''} (t) - 5 f (t)

Solve linear ODE:

f (t) = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

f (t) = c_{1} cos (\frac{5}{3} t) + c_{2} sin (\frac{5}{3} t)

y^{^{''}} - 6 y^{^{'}} + 16 y = 0

y^{^{''}} - 4 y^{^{'}} + 13 y = 0, y (0) = - 1, y^{^{'}} (0) = 5

3 y^{^{''}} + 2 y^{^{'}} + \frac{1}{4} y = 0

(D - 1) (D + 1) (D - 2) x = 0

y^{^{''}} + 4 y^{^{'}} + 4 y = 0, y (0) = 2, y^{^{'}} (0) = 1

What is the solution for 6f^{''}(t)=3f^{''}(t)-5f(t) ?
The solution for 6f^{''}(t)=3f^{''}(t)-5f(t) is f(t)=c_{1}cos(sqrt(5/3)t)+c_{2}sin(sqrt(5/3)t)