Find an explicit solution of the given initial-value problem. dy/dx = ye^x^2, y(3) = 1.

Step-by-step explanation:

This is a separable equation with an initial value i.e. y(3)=1.

Take y from right hand side and divide to left hand side ;Take dx from left hand side and multiply to right hand side:

Take t as a dummy variable, integrate both sides with respect to "t" and substituting x=t (e.g. dx=dt):

Integrate on both sides:

Use initial condition i.e. y(3) = 1:

Taking exponents on both sides to remove "ln":