# Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1. - Mathematics

Sum

Find the particular solution of the differential equation dy/dx=1 + x + y + xy, given that y = 0 when x = 1.

#### Solution

dy/dx=1+x+y+xy

dy/dx = 1 + x + y + xy

dy/dx = 1( 1 + x ) + y ( 1 + x)

dy/dx=(1+x)(1+y)

dy/(1+y)=(1+x)dx

Integrating both sides:

intdy/(1+y)=int(1+x)dx

log|1+y|=x+x^2/2+C

y = 0 when  x = 1     (given)

log1=1+1/2+C

C=−3/2

⇒log|1+y|=x+x^2−3/2 is the required solution.

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