What is the solution for x^3y^'+x^2y=x^7y^{3/4} ?

The solution for x^3y^'+x^2y=x^7y^{3/4} is

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x^3y^'+x^2y=x^7y^{3/4}

x^{3} y^{^{'}} + x^{2} y = x^{7} y^{\frac{3}{4}}

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

Solution steps

x^{3} y^{'} (x) + x^{2} y = x^{7} y^{\frac{3}{4}}

Solve Bernoulli ODE:

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

\frac{d}{d x} (- 7 e^{- 7 x})

x \to 4 lim (ln (x + 2))

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

\frac{\partial}{\partial x} (z arctan (\frac{y}{x}))

\int sin (3 x - 2) d x

What is the solution for x^3y^'+x^2y=x^7y^{3/4} ?
The solution for x^3y^'+x^2y=x^7y^{3/4} is