What is the solution for y^{''}-6y^'+9y=3xe^{3x} ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-6y^'+9y=3xe^{3x}

y^{^{''}} - 6 y^{^{'}} + 9 y = 3 x e^{3 x}

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

Solution steps

y^{''} (x) - 6 y^{'} (x) + 9 y = 3 x e^{3 x}

Solve linear ODE:

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

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

\int (cos (3 x)) d x

\frac{\partial}{\partial x} (2 x - x^{2} y + x y^{2})

\int 5 cos^{2} (x) sin (2 x) d x

\frac{d}{d x} (sin (9))

x \to 0 lim (e^{x s i n (\frac{1}{x})})

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