y/x (dy)/(dx)=sqrt((1+x^2)(1+y^2))

Lösung

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

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

Schritte zur Lösung

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

Solve separable ODE:

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

y = \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}, y = - \frac{3 x ^{4} + 3 x ^{2} + 6 c _{1} ( x ^{2} + 1 ) ^{\frac{3}{2}} + x ^{6} + 9 c _{1}^{2} - 8}{3}

x \frac{d y}{d x} - y ln (y) = 0

15.158 y^{^{'}} + y = 0, y (0) = 14.855

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

\frac{d y}{d x} = x y^{2} e^{x}

\frac{d y}{d x} = \frac{[ ( x ^{2} ) ( y ^{2} ) ]}{5}