(dx)/(dt)=5x-3,x(2)=1

Lösung

\frac{d x}{d t} = 5 x - 3, x (2) = 1

x = \frac{2 e ^{5 t - 10}}{5} + \frac{3}{5}

Schritte zur Lösung

\frac{d x}{d t} = 5 x - 3

Solve separable ODE:

x = \frac{2 e ^{5 t - 10}}{5} + \frac{3}{5}

x = \frac{2 e ^{5 t - 10}}{5} + \frac{3}{5}

\frac{d y}{d x} = 5 x (y^{2})

\frac{d y}{d x} + 4 y = 12

x d y - (y + 1) d x = 0

\frac{d y}{d x} = - \frac{3}{4} x^{4} y^{2}

y^{^{'}} = 12 x y - 2 x, y (0) = 17