1/(y+sqrt(y))dy= 1/(x+sqrt(x))dx

Lösung

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

y = e^{c_{1}} x + 2 e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

Schritte zur Lösung

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

Solve separable ODE:

y = e^{c_{1}} x + 2 e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

y = e^{c_{1}} x + 2 e^{c_{1}} x - 2 e^{\frac{c _{1}}{2}} x + e^{c_{1}} - 2 e^{\frac{c _{1}}{2}} + 1

d y + sin (x) y d x - sin (x) d x = 0

\frac{( d y )}{( d t )} = 2 t cos^{(2)} (y)

(x^{2} + 4) \frac{d y}{d x} + x y = 2 x, y (0) = 3

\frac{d x}{d t} = x sin (t), x (0) = 3

x y^{^{'}} = \frac{3 y ^{3} + 12 y x ^{2}}{2 y ^{2} + 8 x ^{2}}