(dy)/(dt)=(te^t)/(ysqrt(1+y^2))

Lösung

\frac{d y}{d t} = \frac{t e ^{t}}{y 1 + 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} - 1, 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} - 1

Schritte zur Lösung

\frac{d y}{d t} = \frac{t e ^{t}}{y 1 + 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} - 1, 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} - 1

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} - 1, 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} - 1

\frac{d}{d x} (- 16 a x^{2} + a + \frac{1}{3})

\int x cos (5) x^{2} d x

d er i v a t i v e y = 2 x sin (x) + x^{2} e^{x}

\frac{d}{d x} (- 2 x^{2} - 5 x + 2)

\int \frac{1}{x ^{2} - 81} d x