Aren't they simply indefinite integration at the basic level? They seem to be the same thing.
Ex.
Find the general solution;
\(\displaystyle \dfrac{dy}{dx} = x^{2} + 1\)
\(\displaystyle \int dy = \int x^{2} + 1 dx\)
\(\displaystyle y = \dfrac{{x}^{3}}{3} + C\)
You do indefinite integration to get the general solution, but the general solution is simply a solved indefinite integration problem. Now, finding a particular solution is something found only in differential equations courses.
Ex.
Find the general solution;
\(\displaystyle \dfrac{dy}{dx} = x^{2} + 1\)
\(\displaystyle \int dy = \int x^{2} + 1 dx\)
\(\displaystyle y = \dfrac{{x}^{3}}{3} + C\)
You do indefinite integration to get the general solution, but the general solution is simply a solved indefinite integration problem. Now, finding a particular solution is something found only in differential equations courses.
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