(dy)/(dt)=(2+3t)sqrt(y)

Lösung

\frac{d y}{d t} = (2 + 3 t) y

y = c_{1} t + t^{2} + \frac{3 t ^{3}}{2} + \frac{3 c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4} + \frac{9 t ^{4}}{16}

Schritte zur Lösung

\frac{d y}{d t} = (2 + 3 t) y

Solve separable ODE:

y = c_{1} t + t^{2} + \frac{3 t ^{3}}{2} + \frac{3 c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4} + \frac{9 t ^{4}}{16}

y = c_{1} t + t^{2} + \frac{3 t ^{3}}{2} + \frac{3 c _{1} t ^{2}}{4} + \frac{c _{1}^{2}}{4} + \frac{9 t ^{4}}{16}

\frac{d y}{d x} = - 7 y

x \frac{d y}{d x} + x^{3} y = 0

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

e^{2 x} \cdot y^{^{'}} = x cos^{2} (y)

(x^{2} + 1) d y + 2 x (2 y - 1) d x = 0