en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

y^{''}=2y+18tan^3(x)

Solution

y^{^{''}} = 2 y + 18 tan^{3} (x)

Solution

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{9 2 e ^{- 2 x} tan ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{9 2 e ^{2 x} tan ^{3} ( x )}{2} d x

Solution steps

y^{''} (x) = 2 y + 18 tan^{3} (x)

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{9 2 e ^{- 2 x} tan ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{9 2 e ^{2 x} tan ^{3} ( x )}{2} d x

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + e^{2 x} \cdot \int \frac{9 2 e ^{- 2 x} tan ^{3} ( x )}{2} d x + e^{- 2 x} \cdot \int - \frac{9 2 e ^{2 x} tan ^{3} ( x )}{2} d x

Popular Examples

y^{''}+2y^'-2y=e^{-2x}(3x^2+5x+2)

5y^{''}+25y^'+1/(10^{-2)}y=10e^{-x/4}

y^{''}+2y^'-35y=13sin(x)-e^{3x}+1

y^{''}+ay^'+y=e^{-4t}

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

Frequently Asked Questions (FAQ)

What is the solution for y^{''}=2y+18tan^3(x) ?
The solution for y^{''}=2y+18tan^3(x) is