en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

Solution steps

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

Solve linear ODE:

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

y = c_{1} + c_{2} e^{- 2 x} + c_{3} e^{2 x} - \frac{1}{4} (x + \frac{1}{4} sinh (4 x)) + e^{- 2 x} \cdot \int \frac{e ^{2 x} cosh ^{2} ( 2 x )}{4} d x + e^{2 x} \cdot \int \frac{e ^{- 2 x} cosh ^{2} ( 2 x )}{4} d x

Popular Examples

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

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

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

(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}

y^{^{''}} - y = e^{x} + 1

2y^{''}+6y^'-20y=2x-3

2 y^{^{''}} + 6 y^{^{'}} - 20 y = 2 x - 3

Frequently Asked Questions (FAQ)

What is the solution for (d^3-4d)y=2cosh^2(2x) ?
The solution for (d^3-4d)y=2cosh^2(2x) is