What is the solution for (dy)/(dx)=7xsqrt(y) ?

The solution for (dy)/(dx)=7xsqrt(y) is y=(49x^4}{16}+\frac{7c_{1}x^2)/4+(c_{1}^2)/4

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(dy)/(dx)=7xsqrt(y)

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

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

Solution steps

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

Solve separable ODE:

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

y = \frac{49 x ^{4}}{16} + \frac{7 c _{1} x ^{2}}{4} + \frac{c _{1}^{2}}{4}

x \to 0 lim (3 x + 4)

\int \frac{cos ^{3} ( x ) + 4}{cos ^{2} ( x )} d x

\int 3 sin^{2} (x) cos^{2} (x) d x

\frac{\partial}{\partial y} (\frac{- x - 7 y}{y ^{2} + 2 x ^{2}})

\int \frac{1}{x ( 1 + x ) ^{2}} d x

What is the solution for (dy)/(dx)=7xsqrt(y) ?
The solution for (dy)/(dx)=7xsqrt(y) is y=(49x^4}{16}+\frac{7c_{1}x^2)/4+(c_{1}^2)/4