Q. 37 E5.0( 1 Vote )

Solve each of the following initial value problems:

, y(0) = 0

Answer :

, y(0) = 0


Given and y(0) = 0









This is a first order linear differential equation of the form



Here, and


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




We have



Hence, the solution of the differential equation is,





We know





However, when x = 0, we have y = 0



0 = (0 + c)e0


0 = (c) × 1


c = 0


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




Thus, the solution of the given initial value problem is


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