What is the solution for (dy)/(dx)=7sqrt(xy) ?

The solution for (dy)/(dx)=7sqrt(xy) is y=(49x^3)/9+(7c_{1}x^{3/2})/3+(c_{1}^2)/4

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(dy)/(dx)=7sqrt(xy)

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

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

y = \frac{49 x ^{3}}{9} + \frac{7 c _{1} x ^{\frac{3}{2}}}{3} + \frac{c _{1}^{2}}{4}

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

f (x) = (7 x - 8)^{2}

\frac{d}{d y} (y - x)

\int (2 e^{x} + 4^{x}) d x

\int e^{u^{2}} d u

What is the solution for (dy)/(dx)=7sqrt(xy) ?
The solution for (dy)/(dx)=7sqrt(xy) is y=(49x^3)/9+(7c_{1}x^{3/2})/3+(c_{1}^2)/4