(dy)/(dx)y=(x^2e^x)/(x^2+e^x)

Lösung

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

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

Schritte zur Lösung

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

Solve separable ODE:

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

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

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

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

y^{^{'}} + 2 y = - 10

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}, y (1) = ln (2)

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