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pdsolve

pdsolve partial differential and fractional differential equation (PDE) for y and system of equations for x(t) and y(t).

Calling Sequence Parameters Description Examples References Source

Calling Sequence

pdsolve(eq)
pdsolve(eq, y)
pdsolve(eq 1, eq 2)

Parameters

eq - equation.
y - default unknown y(x).
x - variable x.
n - the nth order of equation.

Description

For first order differential equation, there are 3 ways to input derivative:
1. y'
2. y(1,x)
3. ds(y) or ds(y,x)
where ds( ) is a derivative holder.

For second order differential equation, there are 3 ways to input derivative:
1. y''
2. y(2,x)
3. ds(y,x,2)
where y'' is two sinlge quote sign, instead one double quote sign.

For fractional order differential equation, there are 2 ways to input derivative:
1. y(0.5,x)
2. ds(y,x,0.5)

Solution can be tested by test( ). If test(solution,eq) give 0, solution satisfy the equation.

Example

Input first order equation:
> y(1,x)=2y
> y'=2y
> ds(y)=2y
Click the pdsolve button to call pdsolve( ):
> pdsolve(y(1,t)-y(1,x)=2y)
> pdsolve(y(1,t)-y'=2y)
> pdsolve(y(1,t)-ds(y)=2y)

Input second order equation:
> y(1,t)-y(2,x)=2y
> ds(y,t)-ds(y,x,2)=2y
> y(1,t)-y''=2y
> pdsolve(ds(y,t)-ds(y,x,2)=2y)
> pdsolve(ds(y,t)-y''=2y)

Input fractional 0.5 order equation:
> ds(y,t,0.5)-ds(y)=2y
> pdsolve(ds(y,t,0.5)-ds(y)=2y)

References

solve, lasolve, rsolve, nsolve, fsolve, dsolve, ﻿