Q25 Find the particular solutions of the following differential equations :

1. y' - y = e^x, given that y = 1 when x = 0
2. y' + y = e^x, given that y = 1/2 when x = 0
3. xy' + y = x log x, given that y =1/4 when x=1
4. xy' - y = log x, given that y = 0 when x = 1
5. (1 + x²)
   dy / dx
   +2xy =
   1 / 1+x²
   , given that y=0 when x = 1
6. dy / dx
   + 2y tan x = sin x, given that y = 0 when x = π/3
7. y' + 2y = e^-2x sin x, given that y = 0 when x =0
8. xy' + y = x cos x + sin x, given that y = 1 when x = π/2

Solution

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