(dy)/(dx)=-(y^2)/(1+y^2)*e^{-x}

Lösung

\frac{d y}{d x} = - \frac{y ^{2}}{1 + y ^{2}} \cdot e^{- x}

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

Schritte zur Lösung

\frac{d y}{d x} = - \frac{y ^{2}}{1 + y ^{2}} \cdot e^{- x}

Solve separable ODE:

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

y = \frac{c _{1} e ^{x} + 1 + ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}, y = \frac{c _{1} e ^{x} + 1 - ( - c _{1} e ^{x} - 1 ) ^{2} + 4 e ^{2 x}}{2 e ^{x}}

\int x (2 x + 5)^{10} d x

\int ln (x) x^{3} d x

\int x (- cos (x + \frac{π}{3}) + cos (x)) d x

f a c t or x^{5} + 2 x^{4} - 11 x^{3} - 12 x^{2} + 36 x

\frac{d}{d x} (- \frac{1}{x ^{2}} - \frac{7}{x})