The Initial Value Problem yâ€²=y^2/3, y(0)=0 has ?

(a) No solution.

(b) Unique solution.

(c) Two solutions.

(d) Infinitely many solutions.

As I understood, one solution is y=0 itself and other solution comes on solving the differential equation as 3y^(1/3)= x+c, on putting the initial conditions, I get the solution as y=(x^3)/27.

Hence my conclusion is the answer is option c) that is only two solutions. Am I correct?

(a) No solution.

(b) Unique solution.

(c) Two solutions.

(d) Infinitely many solutions.

As I understood, one solution is y=0 itself and other solution comes on solving the differential equation as 3y^(1/3)= x+c, on putting the initial conditions, I get the solution as y=(x^3)/27.

Hence my conclusion is the answer is option c) that is only two solutions. Am I correct?

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