(ye^{xy}cos(2x)-2e^{xy}sin(2x)+2x)+(xe^{xy}cos(2x)-3)y^'=0

Lösung

(y e^{x y} cos (2 x) - 2 e^{x y} sin (2 x) + 2 x) + (x e^{x y} cos (2 x) - 3) y^{^{'}} = 0

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

Schritte zur Lösung

(y e^{x y} cos (2 x) - 2 e^{x y} sin (2 x) + 2 x) + (x e^{x y} cos (2 x) - 3) y^{'} (x) = 0

Solve exact ODE:

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

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

x \to 0 lim ((1 - 6 x)^{\frac{5}{x}})

\frac{d y}{d x} - sin (x) y = 2 sin (x)

d er i v a t i v e g (t) = 5 (cos (π t))^{2}

\frac{d y}{d x} = 2 x - 1 + 2 x y - y

s l o p e (- 19.7, 10.5), (- 18.9, 3.4)