Verify that the functiony=acosx+bsinx, where, a, b∈Ris a solution of the differential equation dx2d2y+y=0.
The differential equations , find the particular solution satisfying the given condition:[xsin2(xy)−y]dx+xdy=0;y=4πwhen x = 1
The differential equations, find a particular solution satisfying the given condition: (x3+x2+x+1)dxdy=2x2+x;y=1when x=0
Form a differential equation representing the given family of curves by eliminating arbitrary constants a and b.y2=a(b2−x2)
In a bank, principal increases continuously at the rate of 5% per year. In how many years Rs 1000 double itself?