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Question

# If the solution of the differential equation dydx=(1+y)2x(1+y)−x2 is λ+yx+c=ln(1+y), then the value of (10λ+6) is equal to

A
10
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B
16
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C
12
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D
14
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Solution

## The correct option is B 16From given differential equations dxdy=x(1+y)−x2(1+y)2 ⇒ dxdy−1(1+y)x=−x2(1+y)2 ⇒ −1x2dxdy+1x.1(1+y)=1(1+y)2, Put 1x=z ⇒ −1x2dxdy=dzdy ∴ dzdy+1(1+y)z=+1(1+y)2 ...(i) I.f. =e∫dx1+y=(1+y) ∴~~Solutions of equations (i) is z×(1+y)=∫+dy(1+y) ⇒ 1+yx+c=ln(1+y) From passing, we get λ=1 ∴ 10λ+6=10×1+6=16

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