Need help solving differential equation?
Solve the differential equation, and find the constant of integration: y' = 3x^2 + 5 and the curve passes through the point (1,8).
- hfshawLv 77 years agoFavorite Answer
y' = dy/dx = 3x^2 + 5
This is a separable equation:
dy = (3x^2 + 5) dx
Integrate both sides:
y(x) = x^3 + 5x + c
where c is the combined constant of integration.
Now use the fact that y(x) passes through (1,8) to determine the value of the constant.
y(1) = 8 = 1 + 5 + c
c = 2
So the particular solution for this case is:
y(x) = x^3 + 5x + 2