y(x) and y cannot both appear in ODE - Maple Help

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Error, (in dsolve) y(x) and y cannot both appear in the given ODE

 

Description

Examples

See Also

Description

This error occurs when both yx and y appear in an ordinary differential equation (ODE), resulting in an ambiguous equation which could mean (for instance) that either the ODE y'+y=0  or the ODE y'+constant=0 is used.

Examples

Example 1
Specifying an equation containing both the function yt and the constant/parameter y is ambiguous because it is not clear whether the ODE y'+y=0  or y'+constant=0 is intended to be used.

dsolvediffyx,x+y=0

Error, (in dsolve) y(x) and y cannot both appear in the given ODE.

 

Solution:

Remove the ambiguity by replacing y with yx.

dsolvediffyx,x+yx=0

yx=_C1ⅇx

(2.1)


Example 2

Similarly, in the following example, it is unclear whether the ODE is meant to be x2y'3 x y'+2 y=x2 or x2y'3 x y'+2 constant=x2. 

 

ode:=x2ⅆ2ⅆt2yt3xⅆⅆtyt+2y=x2

ode:=x2ⅆ2ⅆt2yt3xⅆⅆtyt+2y=x2

(2.2)

IC  y0 = 7, Dy1 = 2

IC:=y0=7,Dy1=2

(2.3)

dsolveode, IC, yt

Error, (in dsolve) y(t) and y cannot both appear in the given ODE.

 

Solution:

Remove the ambiguity by replacing y in ode with yt.

 

ode:=x2ⅆ2ⅆt2yt3xⅆⅆtyt+2yt=x2

ode:=x2ⅆ2ⅆt2yt3xⅆⅆtyt+2yt=x2

(2.4)

IC  y0 = 7, Dy1 = 2

IC:=y0=7,Dy1=2

(2.5)

dsolveode, IC, yt

yt=12x2+124x14ⅇ1x+ⅇ1xx2ⅇ2tx2ⅇ2xⅇ1xⅇtx14ⅇ2x+x2ⅇ2x+2x2ⅇ2xⅇ1x

(2.6)

See Also

dsolve, diff