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Solve: (3xy+y 2 ) dx + (x 2 + xy) dy = 0 Please give the steps after integration begins. PS. ignore the previous ques....there was a mistake of square!


Solve:  (3xy+y2) dx + (x2 + xy) dy = 0


Please give the steps after integration begins.



 


PS. ignore the previous ques....there was a mistake of square!

Grade:12

1 Answers

raj razi
31 Points
8 years ago

dy/dx=-(3xy+y2)/(x2+xy)

put y=vx

dy/dx=v+x(dv/dx)

v+x(dv/dx)=-(3vx2+v2x2)/(x2+vx2)

v+x(dv/dx)=-(3v+v2)/(1+v)

x(dv/dx)=-4v/(1+v)

∫((1+v)/v)dv=-∫(4/x)dx

ln(v)+v=-4lnx+c

(ln(v)+v+lnx4)=constant

ln(y/x)+lnx4+(y/x)=c.

 

 

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