What is the solution for (dy)/(dx)=y(8x^2+1) ?

The solution for (dy)/(dx)=y(8x^2+1) is y=e^{(8x^3)/3+x+c_{1}}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=y(8x^2+1)

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

y = e^{\frac{8 x ^{3}}{3} + x + c_{1}}

Solution steps

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

Solve separable ODE:

y = e^{\frac{8 x ^{3}}{3} + x + c_{1}}

y = e^{\frac{8 x ^{3}}{3} + x + c_{1}}

\frac{1}{y ^{2}} - \frac{3 x}{y ^{3}} \frac{d y}{d x} = 0

y^{^{'}} = 2^{x - y}

y^{2} y^{^{'}} = 2 (t + t y^{3}) e^{t^{2}}, y (0) = 0

y^{^{'}} (x) = \frac{2 x - 1}{3 y ^{2} - 3}, y (1) = 0

\frac{d y}{d x} = \frac{2}{y}

What is the solution for (dy)/(dx)=y(8x^2+1) ?
The solution for (dy)/(dx)=y(8x^2+1) is y=e^{(8x^3)/3+x+c_{1}}