(dy)/(dx)=((xe^x)/(ysqrt(9+y^2)))

Lösung

\frac{d y}{d x} = (\frac{x e ^{x}}{y 9 + y ^{2}})

y = 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9, y = - 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9

Schritte zur Lösung

\frac{d y}{d x} = (\frac{x e ^{x}}{y 9 + y ^{2}})

Solve separable ODE:

y = 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9, y = - 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9

y = 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9, y = - 3 18 c_{1} e^{x} x + 9 e^{2 x} x^{2} - 18 e^{2 x} x - 18 c_{1} e^{x} + 9 e^{2 x} + 9 c_{1}^{2} - 9

\int (3 x) d x

\int x (x^{2} + 6)^{4} d x

n = 1 \sum \infty \frac{n}{e ^{3 n}}

\int (2 x + 3)^{\frac{1}{2}} d x

\frac{d}{d x} (\frac{x ^{4}}{16} + \frac{1}{2 x ^{2}})