Question

Find a solutioin y(x) of the initial value problem dy/dx=3x^2(y-2)^(4/3) y(1)=2. Does this problem have any other solutions? Reference to Existence-Uniqueness Theorem Find a solutioin y(x) of the initial value problem dy/dx=3x^2(y-2)^(4/3) y(1)=2. Does this problem have any other solutions? Reference to Existence-Uniqueness Theorem @Mathematics

Answer 1

I fail to see why the only solution is y(x)=2. If you plug 2 directly into the equation it causes everything to become zero. I tried to use separable equations and got -3/(y-2)^(1/3)+c=x^3 and clearly you can't put the initial conditions in b/c then we'd have a denominator of 0