What is the solution for y^{''}-9y=9e^3x-6x^4 ?

The solution for y^{''}-9y=9e^3x-6x^4 is y=c_{1}e^{3x}+c_{2}e^{-3x}+(2x^4)/3+(8x^2)/9-e^3x+16/81

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-9y=9e^3x-6x^4

y^{^{''}} - 9 y = 9 e^{3} x - 6 x^{4}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{2 x ^{4}}{3} + \frac{8 x ^{2}}{9} - e^{3} x + \frac{16}{81}

Solution steps

y^{''} (x) - 9 y = 9 e^{3} x - 6 x^{4}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{2 x ^{4}}{3} + \frac{8 x ^{2}}{9} - e^{3} x + \frac{16}{81}

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} + \frac{2 x ^{4}}{3} + \frac{8 x ^{2}}{9} - e^{3} x + \frac{16}{81}

y^{^{'''}} - y^{^{''}} = x + e^{x}

y^{^{''}} - 3 y^{^{'}} - 4 y = sin (x)

y^{^{''}} + 4 y^{^{'}} + 32 y = 4 cos (4 t)

y^{^{''}} + 4 y = t^{2} + 6 e^{t}, y (0) = 0, y^{^{'}} (0) = 7

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

What is the solution for y^{''}-9y=9e^3x-6x^4 ?
The solution for y^{''}-9y=9e^3x-6x^4 is y=c_{1}e^{3x}+c_{2}e^{-3x}+(2x^4)/3+(8x^2)/9-e^3x+16/81