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Student[ODEs]

  

Test

  

test the validity of a candidate solution to an ODE

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

Test(sol, ODE, var)

Parameters

sol

-

equation, or set or list of equations; a candidate solution of an ODE or system of ODEs

ODE

-

equation, or set or list of equations; an ODE or system of ODEs

var

-

function, or set or list of functions; the dependent variable(s)

Description

• 

The Test(sol, ODE, y(x)) tests whether the candidate solution sol is in fact a valid solution of the given equation or system ODE.

• 

The equation or system ODE is evaluated using the supplied candidate solution sol, and an attempt is made to remove all occurrences of the dependent variables var and their derivatives; whatever remains is then simplified and returned.

• 

If this remainder is 0 (or a set or list of zeros), then sol is in fact a valid solution.

• 

Conversely, if sol is in fact a valid solution, then this remainder must be mathematically equivalent to 0 (or a set or list of zeros), but it may not have been simplified fully.

Examples

withStudentODEs:

ode1t2zt+1+zt2t1diffzt,t=0

ode1t2zt+1+zt2t1ⅆⅆtzt=0

(1)

sol1Solveode1,zt

sol1zt22zt+lnzt+1=t22tlnt1+_C1

(2)

Testsol1,ode1,zt

0

(3)

ode2diffyx,x,xdiffyx,xxexpx=0

ode2ⅆ2ⅆx2yxⅆⅆxyxxⅇx=0

(4)

sol2Solveode2,yx

sol2yx=_C1+_C2ⅇx+ⅇxx22x+22

(5)

Testsol2,ode2,yx

0

(6)

ode3diffyx,x,x+5diffyx,x2yx=0

ode3ⅆ2ⅆx2yx+5ⅆⅆxyx2yx=0

(7)

sol3Solveode3,yx

sol3yx=6ⅇ_C1x+6_C216,yx=6ⅇ_C1x+6_C216

(8)

Testsol3,ode3,yx

0

(9)

ode4x3diffyx,x,x,x+3x2diffyx,x,x6xdiffyx,x6yx=0

ode4x3ⅆ3ⅆx3yx+3x2ⅆ2ⅆx2yx6xⅆⅆxyx6yx=0

(10)

sol4Solveode4,yx

sol4yx=3_C2x3_C1x2_C3x2

(11)

Testsol4,ode4,yx

0

(12)

ode5diffy1x,x=7y1x+y2x,diffy2x,x=4y1x+3y2x

ode5ⅆⅆxy1x=7y1x+y2x,ⅆⅆxy2x=4y1x+3y2x

(13)

sol5Solve:-Systemode5,output=solution

sol5y1x=ⅇ5x2_C2x+2_C1+_C24,y2x=ⅇ5x_C2x+_C1

(14)

Testsol5,ode5,seqyjx,j=1..2

0

(15)

Compatibility

• 

The Student[ODEs][Test] command was introduced in Maple 2021.

• 

For more information on Maple 2021 changes, see Updates in Maple 2021.

See Also

odetest

Student

Student[ODEs]

Student[ODEs][Solve]