What is the solution for (dy)/(dx)=x^4(y-3),y(0)=9 ?

The solution for (dy)/(dx)=x^4(y-3),y(0)=9 is y=6e^{(x^5)/5}+3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=x^4(y-3),y(0)=9

\frac{d y}{d x} = x^{4} (y - 3), y (0) = 9

y = 6 e^{\frac{x ^{5}}{5}} + 3

Solution steps

\frac{d y}{d x} = x^{4} (y - 3)

Solve separable ODE:

y = 6 e^{\frac{x ^{5}}{5}} + 3

y = 6 e^{\frac{x ^{5}}{5}} + 3

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

\frac{d y}{d x} = - \frac{8}{4} x^{3} y^{5}

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

[k \cdot f (x)] = k \cdot f^{^{'}} (x)

y^{^{'}} = \frac{1}{4} y^{2}

What is the solution for (dy)/(dx)=x^4(y-3),y(0)=9 ?
The solution for (dy)/(dx)=x^4(y-3),y(0)=9 is y=6e^{(x^5)/5}+3