y^'=2.25sqrt(y)

解答

y^{^{'}} = 2.25 y

y = \frac{81 t ^{2}}{64} + \frac{9 c _{1} t}{8} + \frac{c _{1}^{2}}{4}

求解步骤

y^{'} (t) = 2.25 y

求解可分离方程:

y = \frac{81 t ^{2}}{64} + \frac{9 c _{1} t}{8} + \frac{c _{1}^{2}}{4}

y = \frac{81 t ^{2}}{64} + \frac{9 c _{1} t}{8} + \frac{c _{1}^{2}}{4}

\frac{d}{d y} (x (y)^{\frac{2}{3}}) + y^{\frac{2}{3}} = a^{\frac{2}{3}}

(x^{2} + 1) y^{^{'}} + 4 x y = 3 x

\frac{d y}{d t} = - 2 k (y^{2} + 2)

y^{^{'}} = \frac{1 + y ^{2}}{x ^{2} y}

x sin (y) d x - (x^{2} + 1) cos (y) d y = 0