What is the solution for (dy)/(dx)=3xsqrt(y),y\ne 0 ?

The solution for (dy)/(dx)=3xsqrt(y),y\ne 0 is y=(9x^4}{16}+\frac{3c_{1}x^2)/4+(c_{1}^2)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dy)/(dx)=3xsqrt(y),y\ne 0

\frac{d y}{d x} = 3 x y, y \neq = 0

y = \frac{9 x ^{4}}{16} + \frac{3 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

\frac{d y}{d x} = 3 x y

Solve separable ODE:

y = \frac{9 x ^{4}}{16} + \frac{3 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{9 x ^{4}}{16} + \frac{3 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

(x + x y^{2}) d x + (2 y + x^{2} y) d y = 0

(x - 4) 2 y - 5 (x - 4) y^{^{'}} + 9 y = 0

\frac{d y}{d x} y = 7 x - 5

3 x y y^{^{'}} + 4 x - 2 = 0

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

What is the solution for (dy)/(dx)=3xsqrt(y),y\ne 0 ?
The solution for (dy)/(dx)=3xsqrt(y),y\ne 0 is y=(9x^4}{16}+\frac{3c_{1}x^2)/4+(c_{1}^2)/4