en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular Calculus >

(dy)/(dx)=8x(6y+5)^{1/2}

Solution

\frac{d y}{d x} = 8 x (6 y + 5)^{\frac{1}{2}}

Solution

y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} + 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}, y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} - 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}

Solution steps

\frac{d y}{d x} = 8 x (6 y + 5)^{\frac{1}{2}}

Solve separable ODE:

y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} + 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}, y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} - 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}

y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} + 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}, y = \frac{- 10 + 9 c _{1}^{2} + 72 c _{1} x ^{2} + 144 x ^{4} - 9 ( 256 x ^{8} + 256 c _{1} x ^{6} + 96 c _{1}^{2} x ^{4} + 16 c _{1}^{3} x ^{2} + c _{1}^{4} ) ^{\frac{1}{2}}}{12}

Graph

Popular Examples

integral of (-38y+25)/(-y(7y-5))

integral of y+z

(d^4)/(dx^4)(18e^{x^2})

limit as x approaches infinity of 2^x-1

derivative of 4e^{-x^4}

Frequently Asked Questions (FAQ)

What is the solution for (dy)/(dx)=8x(6y+5)^{1/2} ?
The solution for (dy)/(dx)=8x(6y+5)^{1/2} is