(dy)/(dx)=(y^2+5xsqrt(x^2+y^2))/(xy)

Lösung

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

y = 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1

Schritte zur Lösung

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

Solve using substitution:

y = 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1

y = 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1 x, y = - x 25 ln^{2} (x) + 10 c_{1} ln (x) + c_{1}^{2} - 1

9 y^{^{''}} - 18 y^{^{'}} + 11 y = 0

x \to - 4 lim (\frac{2 x + 3}{x + 4})

\frac{d}{d x} ((a - x) a + x)

\frac{d}{d x} (e^{2 x} cos (π x))

\int sin (ln (8 x)) d x