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Question

Find general solution of differential solution given below:
(1+y2)dx=(tan1yx)dy

A
x=cearccoty+arccoty1
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B
x=cearctany+arctany+1
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C
x=cearccoty+arccoty+1
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D
x=cearctany+arctany1
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Solution

The correct option is D x=cearctany+arctany1
(1+y2)dx=(tan1yx)dy
Substitute t=tan1ydt=11+y2dy
(1+y2)dx=(tx)(1=y2)dt
dxdt+x=t
I.F =e1dt=et
Thus solution is, x.et=tetdt+c=tetet+c
x=cearctany+arctany1

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