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) vii) viii) General solution : For the differential equation in the form of General solution is given by, Where, integrating factor, Answer : Given differential equation is Dividing above equation by x, ………eq(1) Equation (1) is of the form Where, and Therefore, integrating factor is ……… ……… ……… General solution is ………eq(2) Let, Put, log x =t => x=et Therefore, (1/x) dx = dt Let, u=t and v=e-t ……… ……… ……… Substituting I in eq(2), Multiplying above equation by x, Therefore, general solution is For particular solution put y=0 and x=1 in above equation, ……… Substituting c in general solution, Therefore, particular solution is