(dy)/(dx)=4y+3e^{8x}(x+1),y(0)=0

Lösung

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1), y (0) = 0

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) - \frac{9}{16} e^{4 x}

Schritte zur Lösung

\frac{d y}{d x} = 4 y + 3 e^{8 x} (x + 1)

Solve linear ODE:

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) - \frac{9}{16} e^{4 x}

y = 3 e^{8 x} (\frac{x}{4} + \frac{3}{16}) - \frac{9}{16} e^{4 x}

x \to 3 - lim (\frac{x + 5}{x - 3})

\int sin^{3} (x) cos^{- 4} (x) d x

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

d er i v a t i v e (12 x^{2} - 24 x + 24) e^{- 8 x}

\int \frac{1}{t ^{2} 64 - t ^{2}} d t