What is the solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 ?

The solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 is y=c_{1}e^{ax}+c_{2}xe^{ax}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 2 a \frac{d y}{d x} + a^{2} y = 0

Solve linear ODE:

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

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

What is the solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 ?
The solution for (d^2y)/(dx^2)-2a(dy)/(dx)+a^2y=0 is y=c_{1}e^{ax}+c_{2}xe^{ax}