86. The general solution of the differential equation (dy / dx) = cos(x + y), with c as a constant, is

1. 1. y + sin (x + y) = x + c

   
   
   

   2. tan			x + y	= y + c
      			2

   
   
   

   3. cos			x + y	= x + c
      			2

   
   
   

   4. tan			x + y	= x + c
      			2

   
   
   

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   Correct Option: D

   
   

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87. The solution of the initial value problem (dy / dx) = – 2xy; y(0) = 2 is

1. 1. 1 + e^-x²

   
   
   

   2. 2e^-x²

   
   
   

   3. 1 + e^x²

   
   
   

   4. 2e^x²

   
   
   

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   Correct Option: B

   
   

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88. Consider the differential equation (dy / dx) = (1 + y²)x. The general solution with constant c is

1. 1. y = tan	x2	+ tanc
      	2

   
   
   

   2. y = tan²			x	+ c
      			2

      
      

   
   
   

   3. y = tan²			x			+ c
      			2

   
   
   

   4. y = tan			x²	+ c
      			2

   
   
   

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   Correct Option: D

   
   

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89. The solution of x		dy	+ y = x4 with the condition y(1) =	6	is
    		dx		5

1. 1. y =	x4	+	1
      	5		x

   
   
   

   2. y =	x4	+	4
      	5		5x

   
   
   

   3. y =	x4	+ 1
      	5

   
   
   

   4. y =	x5	+ 1
      	5

   
   
   

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   Correct Option: A

   
   

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90. The solution of dy/dx = y² with initial value y(0) = 1 bounded in the interval

1. 1. –∞ ≤ x ≤ ∞

   
   
   

   2. –∞ ≤ x ≤ 1

   
   
   

   3. x < 1, x >1

   
   
   

   4. –2 ≤ x ≤ 2

   
   
   

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   Correct Option: C

   
   

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