Questions
Solve the differential equation
a
1xtanlnCx
b
1xcotlnCx
c
1xsinlnCx
d
1xcoslnCx
detailed solution
Correct option is A
Given differential equation is 1−xy+x2y2dx=x2dy⇒1−xy+xy2dx=x2dy .......(i) Substituting xy=v⇒y=vx and dydx=xdvdx−vx2 i.e., x2dy=xdv−vdx in (i), we have 1−v+v2dx=xdv−vdx⇒1+v2dx=xdv⇒∫dv1+v2=∫dxx⇒tan−1v=ln|x|+lnC⇒tan−1v=ln|Cx|⇒v=tanln|Cx|⇒xy=tanln|Cx|⇒y=1xtan(ln|Cx|)Talk to our academic expert!
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The general solution of the differential equation is
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