(dy)/(dx)y= 2/3 x^{2/3}+6x^3

Lösung

\frac{d y}{d x} y = \frac{2}{3} x^{\frac{2}{3}} + 6 x^{3}

y = \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}, y = - \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}

Schritte zur Lösung

\frac{d y}{d x} y = \frac{2}{3} x^{\frac{2}{3}} + 6 x^{3}

Solve separable ODE:

y = \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}, y = - \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}

y = \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}, y = - \frac{4}{5} x^{\frac{5}{3}} + 3 x^{4} + c_{1}

y e^{y} d y = \frac{1 + e ^{- 2 x}}{e ^{x}} d x

y^{^{'}} sec (x) = 7 y^{2}, y (\frac{9 π}{2}) = \frac{1}{4}

x (1 + y^{2}) d x - y (1 + y^{2}) d y = 0

\frac{d y}{d x} = - y^{2}, y (1) = \frac{1}{2}

\frac{d y}{d x} = \frac{1}{y}