What is the solution for y^{''}-4y^'+4y=e^{2x}-6 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-4y^'+4y=e^{2x}-6

y^{^{''}} - 4 y^{^{'}} + 4 y = e^{2 x} - 6

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

Solution steps

y^{''} (x) - 4 y^{'} (x) + 4 y = e^{2 x} - 6

Solve linear ODE:

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

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

y^{^{''}} - y^{^{'}} - 2 y = 1 + t, y (0) = 2, y^{^{'}} (0) = 0

\frac{5}{3} y^{^{''}} + 10 y^{^{'}} + 30 y = 300

3 y^{^{''}} - 4 y^{^{'}} + y = x - 7

\frac{d ^{2} y}{d x ^{2}} + y = sec (x)

y^{^{''}} - 6 y^{^{'}} + 9 y = 2 e^{3 x}

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