ydy=x(1+x^2)^{(-1)/2}(1+y^2)^{1/2}dx

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

y^{^{'}} sec (x) = y^{2}, y (\frac{13 π}{2}) = \frac{1}{3}

\frac{d y}{d x} = - 16 x y

(\frac{y}{x + 6 x}) + (ln (x) - 2) y^{^{'}} = 0

\frac{d y}{d x} = e^{3 x - 5 y}

\frac{d y}{d x} = \frac{( 1 + 4 y ^{2} )}{e ^{x}}