(dy)/(dx)=(y^2+4xsqrt(x^2+y^2))/(xy)

Lösung

\frac{d y}{d x} = \frac{y ^{2} + 4 x x ^{2} + y ^{2}}{x y}

y = 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1

Schritte zur Lösung

\frac{d y}{d x} = \frac{y ^{2} + 4 x x ^{2} + y ^{2}}{x y}

Solve using substitution:

y = 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1

y = 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 16 ln^{2} (x) + 8 c_{1} ln (x) + c_{1}^{2} - 1

f (x) = \frac{1}{x ^{5}}

d er i v a t i v e f (x) = (x^{3} - 3 x) (2 x^{2} + 3 x + 5)

\int 2 sin (θ) - sec^{2} (θ) d θ

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

\int_{- 1}^{1} 3 e^{- 3 x} d x