What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=3x ?

The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=3x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/2+5/12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

(d^2y)/(dx^2)-5(dy)/(dx)+6y=3x

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 3 x

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{2} + \frac{5}{12}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = 3 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{2} + \frac{5}{12}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x}{2} + \frac{5}{12}

What is the solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=3x ?
The solution for (d^2y)/(dx^2)-5(dy)/(dx)+6y=3x is y=c_{1}e^{3x}+c_{2}e^{2x}+x/2+5/12