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A body from rest against a resistance proportional to the square root of the speed at any instant. If the limiting speed is 12m/s, find the time required to attain a speed of 7.15m/s.
Solve the equation :
(7y-3x+3) dy +(3y-7x+7) dx=0
Solve :
x²y" -2xy' -4y=x²+2ln x
Solve :
dy/dx= 1/x+y+1
Solve (P+q) (px+qy) =1, using Charpit's method
Solve :
P² -2xyp + 4y²=0, where p=dy/dx
Solve :
x².d²y/dx² -x. dy/dx +y= ln x
Using the method of variation of parameters, solve the equation:
d²y/dx² +a²y = sec ax.
Solve:
x²y²(2ydx + xdy) - (5ydx + 7xdy) =0
If f(x, y) ={ 1 if x=0 or y=0 and 0 , otherwise } then lim f(x, y) does not exist for limit (x, y) approaches to (0, 0).
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