(dh)/(dt)=-3/100 sqrt(h-15)

解答

\frac{d h}{d t} = - \frac{3}{100} h - 15

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 15

求解步骤

\frac{d h}{d t} = - \frac{3}{100} h - 15

求解可分离方程:

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 15

h = \frac{9 t ^{2} + 9 c _{1}^{2}}{40000} + \frac{9 c _{1} t}{20000} + 15

x^{2} (H (x) x) (H (x) d x + x d H (x)) = 0

4 y^{2} (x d y + y d x) = y d x - x d y

x y^{2} y^{^{'}} = x + 7

y^{^{'}} - x y = 5 x

y ln (x) \frac{d}{d y} (x) = (\frac{y + 1}{x})^{2}, y = 5, x = 4