(y-xy^2)dx-(x+x^2y)dy=0
Answers
Answered by
2
Step-by-step explanation:
ANSWER
⇒x(y
2
+1)dx+y(x
2
+1)dy=0
⇒(
x
2
+1
2x
)dx+(
y
2
+1
2y
)dy=0
let
t=x
2
+1>
⇒dt=2xdx
k=y
2
+1
⇒dk=2ydy
⇒∫
t
dt
+∫
k
dk
=log c
⇒kt=c
⇒(x
2
+1)(y
2
+1)=c
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Answered by
7
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ANSWER
⇒x(y 2 +1)dx+y(x 2 +1)dy=0
⇒( x 2 +12x )dx+( y 2 +12y )dy=0
let t=x 2 +1>
⇒dt=2xdxk=y 2 +1
⇒dk=2ydy
⇒∫tdt +∫ kdk =log c
⇒kt=c
⇒(x 2 +1)(y 2 +1)=c
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