What is the solution for (dy)/(dx)=x^2(y-6),y(0)=8 ?

The solution for (dy)/(dx)=x^2(y-6),y(0)=8 is y=2e^{(x^3)/3}+6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=x^2(y-6),y(0)=8

\frac{d y}{d x} = x^{2} (y - 6), y (0) = 8

y = 2 e^{\frac{x ^{3}}{3}} + 6

Solution steps

\frac{d y}{d x} = x^{2} (y - 6)

Solve separable ODE:

y = 2 e^{\frac{x ^{3}}{3}} + 6

y = 2 e^{\frac{x ^{3}}{3}} + 6

\frac{d y}{d x} - 2 cos (x) y = 0

y^{\frac{1}{2}} y^{^{'}} = 1 - y^{\frac{3}{2}}

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

\frac{d y}{d x} = \frac{( 5 x ^{6} )}{y ^{2}}, y (0) = 1

e^{x^{2}} \frac{d y}{d x} + e^{x^{2}} 2 x y = e^{x^{2}} 2 x

What is the solution for (dy)/(dx)=x^2(y-6),y(0)=8 ?
The solution for (dy)/(dx)=x^2(y-6),y(0)=8 is y=2e^{(x^3)/3}+6