(dy)/(dt)=(te^t)/(ysqrt(6+y^2))

Lösung

\frac{d y}{d t} = \frac{t e ^{t}}{y 6 + y ^{2}}

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6

Schritte zur Lösung

\frac{d y}{d t} = \frac{t e ^{t}}{y 6 + y ^{2}}

Solve separable ODE:

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6

y = 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6, y = - 3 18 c_{1} e^{t} t + 9 e^{2 t} t^{2} - 18 e^{2 t} t - 18 c_{1} e^{t} + 9 e^{2 t} + 9 c_{1}^{2} - 6

ma c l a u r in e^{\frac{x}{2}}

x \to \infty lim (1 - 2^{x})

\frac{d}{d x} (ln (π))

\int_{0}^{3} (3 t + 4) d t

\int_{- 1}^{1} ln ∣ x ∣ d x