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Verify that y=(c-x)/(1+cx) is a solution...

Verify that `y=(c-x)/(1+cx)` is a solution of the differential equation `(1+x^(2))(dy)/(dx)+(1+y^(2))=0.`

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Let c = tan A and x=tan B. Then.
`y=(tanA-tanB)/(1+tanAtanB)=tan(A-B)impliestan^(-1)y=A-B`
`impliestan^(-1)y=tan^(-1)(c) -tan^(-1)x`
`implies(1)/((1+y^(2)))(dy)/(dx)=0-(1)/((0+x^(2)))`
`implies(1+x^(2))(dy)/(dx)+(1+y^(2))=0.`
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RS AGGARWAL-DIFFERENTIAL EQUATIONS AND THEIR FORMATION -Exercise 18B
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  13. Verify the solution problems: Show that y = e^-x + ax +b is solution o...

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  14. Show that A x^2+B y^2=1 is a solution of the differential equation x{y...

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  15. Verify that y=(c-x)/(1+cx) is a solution of the differential equation ...

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  16. Verify that y=log(x+sqrt(x^2+a^2)) satisfies the differential equation...

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  17. Verify that the function y=e^(-3x)is a solution of the differential eq...

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