The initial value problem $\dfrac{dx}{dt}=x^{\frac{3}{2}}(t),~x(0)=0$ has

Question

The initial value problem $\dfrac{dx}{dt}=x^{\frac{3}{2}}(t),~x(0)=0$ has

A) Unique solution

B) Two solution

C) Infinitely many solution

D) None of the above

$\textbf{My try}$

As we know for $x=0$ is the one solution, let's see for other solutions

$\int x^{-\frac{3}{2}} dx~=~\int dt$

After some simplification

$\sqrt{x}=-\dfrac{2}{t+c}$

After applying $x(0)=0$ we got $-\dfrac{2}{c}=0$.

Which means option C is wrong. And option A is correct. But according to answer key, answer is $\textbf{infinite number of solutions}$. Please help me.