For the differential equation ydx+y2dy=xdy,x∈R,y(1)=1, then the value of y(−3) is:
A
3
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B
4
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C
−1
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D
−2
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Solution
The correct option is C−1 The given equation is ydx+y2dy=xdy;x∈R,y(1)=1 ⇒ydx−xdyy2+dy=0 ⇒d(xy)+dy=0
On integrating, we get xy+y=C y(1)=1⇒1+1=C⇒C=2 ∴xy+y=2
Now to find y(−3), putting x=−3 in the above equation
we get, −3y+y=2 ⇒y2−2y−3=0⇒y=3,−1