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先翻译下
(1)
Solve the separable differential equation
dy/dt=8y^4
and find the particular solution satisfying the initial condition
y(0)=-6,y(t)=?
求微分方程dy/dt=8y^4的解并且找到满足初始条件y(0)=-6的特定的解.
(2)
Find the solution to the differential equation
dy/dt=y^2(6+t)
y=8whent=1
求微分方程dy/dt=y^2(6+t)的解当t=1时y=8.
solution：
(1)dy/dt=8y^4
[1/(8y^4)]dy=dt
-1/24*y^-3=t+C
Into the y(0)=-6 get C=6
so -1/(24y^3)=t+6
(2)dy/dt=y^2(6+t)
y^-2 dy=(6+t) dt
-y^-1=6t+1/2 t^2+C
y=8whent=1 get C=-53/8
so -1/y=6t+1/2 t^2-53/8