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

The solution for y^{''}-5y^'+6y=x^2+x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(4x)/9+17/54

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

y = c_{1} e^{3 x} + c_{2} e^{2 x} + \frac{x ^{2}}{6} + \frac{4 x}{9} + \frac{17}{54}

(d^{2} - 4 d + 4) \cdot y = 12 \cdot (1 + x)^{2} \cdot e^{2 x}

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

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

(d - 1)^{2} \cdot y = sin (x) \cdot x^{2} \cdot e^{x}

(d^{3} + 1) \cdot y = cos (2 x - 1)

What is the solution for y^{''}-5y^'+6y=x^2+x ?
The solution for y^{''}-5y^'+6y=x^2+x is y=c_{1}e^{3x}+c_{2}e^{2x}+(x^2)/6+(4x)/9+17/54