Q. 37 A5.0( 1 Vote )

Solve each of the following initial value problems:

y’ + y = ex,

Answer :

y’ + y = ex,


Given y’ + y = ex and




This is a first order linear differential equation of the form



Here, P = 1 and Q = ex


The integrating factor (I.F) of this differential equation is,




We have


I.F = ex


Hence, the solution of the differential equation is,






Recall






However, when x = 0, we have




c = 0


By substituting the value of c in the equation for y, we get




Thus, the solution of the given initial value problem is


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