how to solve the differential equation $\frac{kx^t}{v^2} + 1=\frac{dv}{dx}$

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I came across the differential equation in physics

how to solve

$\frac{kx^{1-\gamma}}{v^2} + 1=\frac{dv}{dx}$

given that

$v'(l)=0,v(l)=c,v(0)=0,\gamma>1$

I tried $\frac{1}{v}=\lambda$ but it was of no avail.

I then tried to set up a taylor series with $c_0=0$ but don't know how to proceed

Is there anyway it can be solved using the stuff taught in high school

please help