What is the solution for y^{''}-6y^'+8y=16x^2-2 ?

The solution for y^{''}-6y^'+8y=16x^2-2 is y=c_{1}e^{4x}+c_{2}e^{2x}+2x^2+3x+3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-6y^'+8y=16x^2-2

y^{^{''}} - 6 y^{^{'}} + 8 y = 16 x^{2} - 2

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 2 x^{2} + 3 x + \frac{3}{2}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = 16 x^{2} - 2

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 2 x^{2} + 3 x + \frac{3}{2}

y = c_{1} e^{4 x} + c_{2} e^{2 x} + 2 x^{2} + 3 x + \frac{3}{2}

(d^{3} - 2 d^{2} - 5 d + 6) y = e^{4} x

(d^{3} - 4 d) y = 2 cosh^{2} (2 x)

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

(d^{4} - 2 d^{3} - 3 d^{2} + 4 d + 4) y = cos (3 x + 5) + (e^{3})^{x}

(d^{2} - 4) y = x^{2}

What is the solution for y^{''}-6y^'+8y=16x^2-2 ?
The solution for y^{''}-6y^'+8y=16x^2-2 is y=c_{1}e^{4x}+c_{2}e^{2x}+2x^2+3x+3/2