Final answer:
The inquiry involves solving a first-order nonlinear differential equation with given initial conditions and finding specific y-values for given x-values.
Step-by-step explanation:
The student has presented a first-order nonlinear differential equation dy/dx = 2x y^2 with given initial conditions. Solving this type of differential equation typically involves separation of variables or an integrating factor, but exact analytical solutions are only sometimes possible. However, in this case, the student seems to be asking for the values of y at specific points given x-values, possibly obtained from the solution to the differential equation or from numerical methods.
Example Solution Process
1. Separate the variables to get the equation into the form y^(-2) dy = 2x dx.
2. Integrate both sides to find the general solution in terms of x.
3. Use the given initial condition to find the constant of integration, C.
4. Evaluate the solution at the given x-values to find y.
Note: Typos or irrelevant parts of the question are ignored, and no exact solution is provided without the appropriate function y(x).