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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!

Shalini Rai , 13 Years ago
Grade 12
anser 1 Answers
raj razi

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.

 

 

Last Activity: 13 Years ago
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