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

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

3 y^{2} d y - t d t = 0

y^{^{'}} + 21 x^{2} y = 21 x^{2}

f^{^{'}} (x) = 7 f (x)

y^{^{'}} = 8 x (y^{2} + 1)

(3 t^{5} + 1) y \frac{d y}{d t} = 4 t^{4}