solve linear differential equations as power series
set or expression sequence containing a linear differential equation and optional initial conditions
The function powsolve solves a linear differential equation for which initial conditions do not have to be specified.
All the initial conditions must be at zero.
Derivatives are denoted by applying D to the function name. For example, the second derivative of y at 0 is D⁡D⁡y⁡0.
The solution returned is a formal power series that represents the infinite series solution.
In some cases, after assigning the name a to the output from the powsolve command, you can enter the command a(_k) to output a recurrence relation for the power series solution. See examples below.
The command with(powseries,powsolve) allows the use of the abbreviated form of this command.
a ≔ powsolve⁡ⅆⅆx⁢y⁡x=y⁡x,y⁡0=1:
v ≔ powsolve⁡ⅆ4ⅆx4⁢y⁡x=y⁡x,y⁡0=32,D⁡y⁡0=−12,D⁡D⁡y⁡0=−32,D⁡D⁡D⁡y⁡0=12:
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