(dy)/(dx)=sqrt(5y)*e^{x+6}

Lösung

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d x} = 5 y \cdot e^{x + 6}

Solve separable ODE:

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

y = \frac{5 e ^{12 + 2 x}}{4} + \frac{5 c _{1} e ^{x + 6}}{2} + \frac{c _{1}^{2}}{4}

\frac{d}{d x} ((ln (x))^{2} (sin (x)))

(x^{2} + 2 x y - 4 y^{2}) d x - (x^{2} - 8 x y - 4 y^{2}) d y = 0

d er i v a t i v e sin (x) cos (x) - sin^{2} (x) + x

x \to 0 lim (\frac{e ^{8 x} - 1}{x})

s l o p e in t erce pt (2, 1), (- 4, - 2)