Question

What is a solution to the differential equation dy/dx= x^2+1? (Please

Answer 1

`y=1/3x^3+x+C`

Explanation:

This is another separable differential equation; however, we have no `y` involved. As a result, we'll keep `dy` on the left, and move all terms involving `x, dx` on the right.

`dy=(x^2+1)dx`

Integrate both sides:

`intdy=int(x^2+1)dx`

`int(x^2+1)dx=intx^2dx+intdx=1/3x^3+x+C`, as `intx^adx=x^(a+1)/(a+1), a ne -1`

Thus, we get

`y=1/3x^3+x+C`