Find a particular solution satisfying the given condition for each of the following differential equations.
, given that Given Differential Equation : Formula : i) ii) iii) iv) v) vi) General solution : For the differential equation in the form of General solution is given by, Where, integrating factor, Answer : Given differential equation is ………eq(1) Equation (1) is of the form Where, and Therefore, integrating factor is ……… ……… General solution is ………eq(2) Let, Let, u=x2 and v= tan x. sec x ……… ……… Substituting I in eq(2), Multiplying above equation by cos x, Therefore, general solution is For particular solution put y=1 and x=0 in above equation, Substituting c in general solution, Therefore, particular solution is