For many applications, a few terms of a Taylor series solution are sufficient. You can control the number of terms that appear in the solution by changing Series Order for ODE Solutions in the Maple Settings dialog. For most of the following examples, the series order has been set at 6.
To specify the order of terms in a series solution
In the following examples, notice that the initial condition y(0) appears explicitly in each solution. Choose Series from the Solve ODE submenu to produce the following solutions.
Solve ODE + Series
Dxy = y, Series solution is : yx
= y
0
+ y
0
x +
y
0
x2 +
y
0
x3 +
y
0
x4 +
y
0
x5 + O
x6
y′ =(Specify x), Series solution is : y
x
= y
0
+ x -
x3 +
x5 + O
x6
+ y = e-x2, Series solution is : y
x
= y
0
+
- y
0
+ 1
x +
y
0
-
x2 +
-
y
0
-
x3 +
y
0
+
x4 +
-
y
0
+
x5 + O
x6
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