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

Lösung

y^{^{'}} = x y^{3} (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} (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} )}

d er i v a t i v e f (x) = (x^{2} + 8) (7 - x)

x \to 1 lim (e^{\frac{1}{x - 1}})

\int \frac{4 x}{3 x} d x

\int_{1}^{4} \frac{2}{x ^{2}} d x

\frac{d}{d x} (sin^{6} (π x))