x^2(dy)/(dx)=sqrt(y)(4x+5)

Lösung

x^{2} \frac{d y}{d x} = y (4 x + 5)

y = - \frac{5 c _{1}}{2 x} - \frac{10 ln ( x )}{x} + \frac{25}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

Schritte zur Lösung

x^{2} \frac{d y}{d x} = y (4 x + 5)

Solve separable ODE:

y = - \frac{5 c _{1}}{2 x} - \frac{10 ln ( x )}{x} + \frac{25}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

y = - \frac{5 c _{1}}{2 x} - \frac{10 ln ( x )}{x} + \frac{25}{4 x ^{2}} + \frac{c _{1}^{2}}{4} + 4 ln^{2} (x) + 2 c_{1} ln (x)

(1 - x) \frac{d y}{d x} - y^{2} = 0

\frac{d y}{d x} = x \cdot y

y^{^{'}} = 3 y e^{t}, y (0) = 1

\frac{d y}{d x} = x^{2} y - 1.1 y

y^{^{'}} = \frac{e ^{- x} - e ^{x}}{3 + 4 y}