(x+1)((dy)/(dx))+(2x-1)y=e^{-2x}

Lösung

(x + 1) (\frac{d y}{d x}) + (2 x - 1) y = e^{- 2 x}

y = - \frac{1}{3 e ^{2 x}} + \frac{c _{1} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{e ^{2 x + 2 + c_{1}}}

Schritte zur Lösung

(x + 1) (\frac{d y}{d x}) + (2 x - 1) y = e^{- 2 x}

Solve linear ODE:

y = - \frac{1}{3 e ^{2 x}} + \frac{c _{1} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{e ^{2 x + 2 + c_{1}}}

y = - \frac{1}{3 e ^{2 x}} + \frac{c _{1} ( x ^{3} + 3 x ^{2} + 3 x + 1 )}{e ^{2 x + 2 + c_{1}}}

x \to - 1 lim ((x + 2 x^{3})^{5})

t an g e n t f (x) = \frac{1}{2} - x^{2}, at x = - \frac{1}{2}

x \to + (- 5) lim (3 x - ∣ x + 5 ∣)

1 - 3 x^{2} y^{^{'}} = x

\frac{\partial}{\partial y} (e^{x^{2} - y^{2} + 4 y})