(x^2+2x-1)y^'-(x-1)y=x-1

Lösung

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

y = e^{c_{1} + \frac{l n ( \frac{x ^{2} - 1}{2} + x ) + 2 ( l n ( 1 + \frac{1}{2} ( 1 + x ) ) - l n ( - 1 + \frac{1}{2} ( 1 + x ) ) )}{2}} - 1

Schritte zur Lösung

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

Solve separable ODE:

y = e^{c_{1} + \frac{l n ( \frac{x ^{2} - 1}{2} + x ) + 2 ( l n ( 1 + \frac{1}{2} ( 1 + x ) ) - l n ( - 1 + \frac{1}{2} ( 1 + x ) ) )}{2}} - 1

y = e^{c_{1} + \frac{l n ( \frac{x ^{2} - 1}{2} + x ) + 2 ( l n ( 1 + \frac{1}{2} ( 1 + x ) ) - l n ( - 1 + \frac{1}{2} ( 1 + x ) ) )}{2}} - 1

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

\frac{d x}{d t} = 50 - \frac{7 x}{100}

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

y^{^{'}} + \frac{1}{2} y = 9

\frac{d y}{d x} = \frac{x}{y}, y (4) = - 3