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Let y = y(x) be the solution of the differential equation, (x2 + 1)2 + 2x (x2+ 1) y = 1 such that y(0) = 0. If  y(1) = , then the value of ‘a’ is

(a)

 

(b)

 

(c)

1

(d)

 


Question ID - 57542 | Toppr Answer

Let y = y(x) be the solution of the differential equation, (x2 + 1)2 + 2x (x2+ 1) y = 1 such that y(0) = 0. If  y(1) = , then the value of ‘a’ is

(a)

 

(b)

 

(c)

1

(d)

 

1 Answer - 5876 Votes

3537

Answer Key : (d) -

(1 + x2) + 2x(1 + x2) y = 1

It is a linear differential equation

I.F. =  = 1 + x2

⇒ y’ (1 + x2) =  + c

⇒ y (= tan − 1 x + c

If x = 0 then y = 0

So, 0 = 0 + c

 ⇒ c = 0

⇒ y (1 + x2) = tan−1 x

put x = 1

2y =

⇒ 2 =

 =

⇒ a =



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