What is the solution for y^{''}-5y^'+6y=x^2+3x ?

The solution for y^{''}-5y^'+6y=x^2+3x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(7x)/9+16/27

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

y^{''}-5y^'+6y=x^2+3x

y^{^{''}} - 5 y^{^{'}} + 6 y = x^{2} + 3 x

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

Solution steps

y^{''} (x) - 5 y^{'} (x) + 6 y = x^{2} + 3 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{7 x}{9} + \frac{16}{27}

What is the solution for y^{''}-5y^'+6y=x^2+3x ?
The solution for y^{''}-5y^'+6y=x^2+3x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(7x)/9+16/27