(xdy)/(dx)=5xe^x-y+6x^2

Lösung

\frac{x d y}{d x} = 5 x e^{x} - y + 6 x^{2}

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 2 x^{2} + \frac{c _{1}}{x}

Schritte zur Lösung

\frac{x d y}{d x} = 5 x e^{x} - y + 6 x^{2}

Solve linear ODE:

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 2 x^{2} + \frac{c _{1}}{x}

y = \frac{5 ( e ^{x} x - e ^{x} )}{x} + 2 x^{2} + \frac{c _{1}}{x}

\int (x^{5} - 4 x)^{2} (5 x^{4} - 4) d x

x \to 0 + lim (\frac{1}{1 + \frac{1}{x}})

\frac{d}{d x} (- 8)

x \to 0 lim (\frac{sin ^{2} ( 3 x )}{5 x ^{2}})

\int sin (4 x) sin (x) d x