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Question

Find the solution of dydx=8x+6y+124x+3y+2.

A
5(3y+6x)12log(20x+15y+22)=k
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B
5(3y6x)12log(20x+15y+22)=k
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C
5(3y5x)12log(20x+15y+22)=k
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D
5(3y+5x)12log(20x+15y+22)=k
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Solution

The correct option is B 5(3y6x)12log(20x+15y+22)=k
Given differential equation
dydx=8x+6y+124x+3y+2 ....(1)
Substitute 4x+3y=v
4+3dydx=dvdx
dydx=13(dvdx4)
So, equation (1) becomes
13(dvdx4)=2v+12v+2
dvdx4=6v+36v+2
v+210v+44dv=dx
10v+2010v+44dv=10dx
(12410v+44)dv=10dx.
(112(5v+22)dv=10dx.
Integrating both sides, we get
v125log(5v+22)=10x+k
or 4x+3y125log(20x+15y+22)=10x+k
or 5(3y6x)12log(20x+15y+22)=c

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