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

Lösung

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}

Schritte zur Lösung

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})

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

d er i v a t i v e x^{2} + 3 x + 4

\int x x + 8 d x

\int 0.0018 h^{2} d h