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Question

18. The general solution of the differential equation e* dy + (y e2x) dx 0 is(A) xexC(C) ye2C

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Solution

The given differential equation is,

e x dy+( y e x +2x )dx=0 dy dx = ( y e x +2x ) e x dy dx = y e x e x 2x e x dy dx +y= 2x e x

The given differential equation is of the form dy dx +Py=Q.

Here,

P=1 Q= 2x e x

Now, calculate the Integrating factor,

IF= e Pdx = e 1dx = e x

The solution of the differential equation is,

y( IF )= ( Q×IF )dx +c y e x = ( 2x e x e x ) dx+c y e x =2 x dx+c y e x =2 x 2 2 +c

Further, simplify the equation,

y e x = x 2 +c y e x + x 2 =c

Hence, the correct option is ©.


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