What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x} ?

The solution for (d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x} is y=c_{1}e^{4x}+c_{2}e^{2x}+4xe^{4x}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x}

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 8 e^{4 x}

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 4 x e^{4 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 6 \frac{d y}{d x} + 8 y = 8 e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 4 x e^{4 x}

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 4 x e^{4 x}

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} = x

y^{^{''}} + 16 y = 3 csc^{2} (4 x)

y^{^{''}} - 4 y^{^{'}} + 3 y = (x^{2} - 3 x) e^{- x}

y^{^{''}} + y = 5

y^{^{''}} + y = 8

What is the solution for (d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x} ?
The solution for (d^2y)/(dx^2)-6(dy)/(dx)+8y=8e^{4x} is y=c_{1}e^{4x}+c_{2}e^{2x}+4xe^{4x}