xy^'+2y=3,xy(1)=5

Lösung

x y^{^{'}} + 2 y = 3, x y (1) = 5

y = - \frac{c _{1}}{2 x ^{2}} + \frac{3}{2}

Schritte zur Lösung

x y^{'} (x) + 2 y = 3

Solve separable ODE:

y = - \frac{c _{1}}{2 x ^{2}} + \frac{3}{2}

y = - \frac{c _{1}}{2 x ^{2}} + \frac{3}{2}

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

y + 5 + (x - 3) \frac{d y}{d x} = 0

\frac{d y}{d x} + (\frac{1 + x}{x}) y = 0

\frac{d y}{d x} = 9 x y

\frac{d x}{d t} = t x