(dv)/(dt)=-0.00353v^2-3

解答

\frac{d v}{d t} = - 0.00353 v^{2} - 3

v = 29.15233 \dots tan (- \frac{t + c _{1}}{9.71744 \dots})

求解步骤

\frac{d v}{d t} = - 0.00353 v^{2} - 3

求解可分离方程:

v = 29.15233 \dots tan (- \frac{t + c _{1}}{9.71744 \dots})

v = 29.15233 \dots tan (- \frac{t + c _{1}}{9.71744 \dots})

\frac{d y}{d t} = - 0.05 y + 0.75

\frac{d y}{d x} = (1 + y^{2}) e^{x}

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

y^{^{'}} + 2 y = 11

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