Answer :

Formula :


i)


ii)


iii)


iv)


v) General solution :


For the differential equation in the form of



General solution is given by,



Where, integrating factor,



Answer :


The slope of the tangent to the curve


The slope of the tangent to the curve is equal to the sum of the coordinates of the point.



Therefore 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=x and v= e-x



………



………


………


Substituting I in eq(2),



Dividing above equation by e-x,



Therefore, general solution is



The curve passes through origin , therefore the above equation satisfies for x=0 and y=0,




Substituting c in general solution,



Therefore, equation of the curve is



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