In the example below, I use Maple's dsolve() function to solve a simple ODE. Then I use Maple to
verify that it is in fact a solution to the ODE by substituting it back into the ODE.
In the example below, I'm solving the ODE y' = 2xy.
(1)
(2)
The Maple output above tells me that my solution to this ODE has the form
y(x) = C*exp(x^2). So in this next part I will define y(x) to be this solution, plug it back into the ODE
and verify that it satisfied the ODE.
The best way in Maple to verify that two quantities are equal to to make sure their difference is zero.
So if RHS represents the right-hand side of an equation, and LHS is the left-hand side of the same
equation, then verifying that LHS=RHS is the same as verifying that LHS-RHS = 0.
(3)
(4)
(5)
0
(6)
The last line of output here verifies that the two sides of the ODE are equal when our definition of y(x)
is substituted.