y^'=xy^3(1+x^2)^{1/2}

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

\frac{d y}{d x} = \frac{y ln ( y )}{x}

x y^{3} d x + e^{- x} d y = 0

\frac{d y}{d x} = x^{2} y, y > 0

\frac{d y}{d x} = \frac{e ^{x} - cos ( 2 x )}{y}, y (0) = 2

y^{^{'}} = x e^{y - x^{2}}, y (0) = 0