Solution of y,dx+(x+x^2y),dy=0 is: · questionr

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Exams
Joint Entrance Examination
Mathematics
Differential Equations
Question 328

Question 328 of 490MediumMCQ

Solution of

y\,dx+(x+x^2y)\,dy=0

is:

A

\log y=Cx

B

-\dfrac{1}{xy}+\log y=C

C

\dfrac{1}{xy}+\log y=C

D

-\dfrac{1}{xy}=C

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Solutions · 1

Official solution

Bernoulli form; with

t=1/x

:

\dfrac{dt}{dy}-\dfrac{t}{y}=1

. I.F.

=1/y

. \[\frac{t}{y} = \ln y+C \implies \frac{1}{xy}=\ln y+C \implies \log y-\frac{1}{xy}=C.\]

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