Answer :

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=sin x and v=e2x



………



………



Again, let u=cos x and v=e2x



………



………








Multiplying above equation by 4,





Substituting I in eq(2),



Dividing above equation by e2x,



Therefore general equation is



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