y^'=5(x-2)y^{1/2}-y/(x-2)

Lösung

y^{^{'}} = 5 (x - 2) y^{\frac{1}{2}} - \frac{y}{x - 2}

y = x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 2 c_{1} (x - 2)^{\frac{3}{2}} + \frac{c _{1}^{2}}{x - 2} + 16

Schritte zur Lösung

y^{'} (x) = 5 (x - 2) y^{\frac{1}{2}} - \frac{y}{x - 2}

Solve Bernoulli ODE:

y = x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 2 c_{1} (x - 2)^{\frac{3}{2}} + \frac{c _{1}^{2}}{x - 2} + 16

y = x^{4} - 8 x^{3} + 24 x^{2} - 32 x + 2 c_{1} (x - 2)^{\frac{3}{2}} + \frac{c _{1}^{2}}{x - 2} + 16

\frac{\partial}{\partial x} (1 x, 4 y)

x \to 1 + lim (1 - cos (2 (x - 1)))

d er i v a t i v e sin (θ) cos (θ)

\int - sec (x) d x

x \to - 27 lim (\frac{6}{x + 27})