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Student[ODEs]

  

LinearForm

  

convert a first order ODE into linear form, if possible

 

Calling Sequence

Parameters

Description

Examples

Compatibility

Calling Sequence

LinearForm(ODE, y(x))

Parameters

ODE

-

an ordinary differential equation

y

-

name; the dependent variable

x

-

name; the independent variable

Description

• 

LinearForm(ODE, y(x)) outputs an equivalent linear ODE, if that is possible. If not, an error is produced.

Examples

withStudentODEs:

ode1t2zt+1zt+t1diffzt,t=t2zt+1zt

ode1t2zt+1zt+t1ⅆⅆtzt=t2zt+1zt

(1)

LinearFormode1,zt

ⅆⅆtzt=t2ztt1t2t1

(2)

ode2t2zt+1+zt2t1diffzt,t=0

ode2t2zt+1+zt2t1ⅆⅆtzt=0

(3)

LinearFormode2,zt

Error, (in Student:-ODEs:-LinearForm) the ODE, t^2*(z(t)+1)+z(t)^2*(t-1)*diff(z(t),t) = 0, does not appear to be linearizable, at least without further simplification.

Compatibility

• 

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

• 

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

See Also

dsolve

Student

Student[ODEs]