What is the solution for y^{''''}-40y^{'''}+400y^{''}=0 ?

The solution for y^{''''}-40y^{'''}+400y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{20t}+c_{4}te^{20t}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''''}-40y^{'''}+400y^{''}=0

y^{^{''''}} - 40 y^{^{'''}} + 400 y^{^{''}} = 0

y = c_{1} + c_{2} t + c_{3} e^{20 t} + c_{4} t e^{20 t}

Solution steps

y^{(4)} (t) - 40 y^{'''} (t) + 400 y^{''} (t) = 0

Solve linear ODE:

y = c_{1} + c_{2} t + c_{3} e^{20 t} + c_{4} t e^{20 t}

y = c_{1} + c_{2} t + c_{3} e^{20 t} + c_{4} t e^{20 t}

\frac{d ^{2} y}{d x ^{2}} + 11 \frac{d y}{d x} + 24 y = 0

x^{^{''}} + 2 x^{^{'}} + 8 x = 0

y^{^{''}} - 15 y^{^{'}} + 50 y = 0

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

0.701 x^{^{''}} + 27.4667 x = 0

What is the solution for y^{''''}-40y^{'''}+400y^{''}=0 ?
The solution for y^{''''}-40y^{'''}+400y^{''}=0 is y=c_{1}+c_{2}t+c_{3}e^{20t}+c_{4}te^{20t}