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The differential equation

$\frac{dy}{dx}= y^{1/3}, y(0)=0$ has

  1. A unique solution
  2. No nontrivial solution 
  3. Finite number of solutions.
  4. Infinite number of solutions. 
asked in Calculus by Veteran (29.1k points)   | 51 views

1 Answer

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dy/dx = y1/3

or,∫dy/(y1/3) =∫dx + c

or, y2/3 /(2/3) = x + c

or,3/2 . y2/3 = x + c

or,3/2 . 0 = 0 + c

or, c=0

or, 3/2 . y2/3 = x 

Now say y=8, x=3/2 . 4 =6

Ans will be (D)

 

answered by Veteran (52.4k points)  


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