(dy)/(dx)=3x^2(1+y^2)^{3/2}

Lösung

\frac{d y}{d x} = 3 x^{2} (1 + y^{2})^{\frac{3}{2}}

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

Schritte zur Lösung

\frac{d y}{d x} = 3 x^{2} (1 + y^{2})^{\frac{3}{2}}

Solve separable ODE:

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

y = \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}, y = - \frac{- x ^{6} - 2 c _{1} x ^{3} - c _{1}^{2}}{- 1 + c _{1}^{2} + 2 c _{1} x ^{3} + x ^{6}}

d er i v a t i v e f (x) = 5 x^{2} - x^{\frac{1}{3}}

\frac{\partial}{\partial x} (e^{z})

n = 1 \sum \infty \frac{3}{2 ^{n} + 1}

\int \frac{ln ( 4 x )}{x ^{3}} d x

f (x) = \frac{( x ^{2} + 9 )}{( x ^{2} - 9 )}