# Question:What is the problem with Maple for this differential equation?

## Question:What is the problem with Maple for this differential equation?

Maple 2020

restart;
deq1 := diff(u(x, y), x) - diff(u(x, y), y\$2) = exp(x+y);
/  2         \
/ d         \   | d          |
deq1 := |--- u(x, y)| - |---- u(x, y)| = exp(x + y)
\ dx        /   |   2        |
\ dy         /

deq2 := diff(u(x, y), x) - diff(u(x, y), y\$2) = exp(1)^(x+y);
/  2         \
/ d         \   | d          |           (x + y)
deq2 := |--- u(x, y)| - |---- u(x, y)| = (exp(1))
\ dx        /   |   2        |
\ dy         /

pdsolve(deq1, u(x,y));  ### no result
pdsolve(deq2, u(x,y));
/
|
PDESolStrucApplyFunction|uApplyFunction(x,y)=_F1ApplyFunction(x)
\

1
_F2ApplyFunction(y) - -
2

x+y
(expApplyFunction(1))    (_C1 expApplyFunction(uminus0y)+_C2 expApplyFunction(y)+_C3 expApplyFunction(y) y)
-----------------------------------------------------------------------------------------------------------
_C3 expApplyFunction(y)

,[{diffApplyFunction(_F1ApplyFunction(x),x)=_c[1] _F1

ApplyFunction(x),diffApplyFunction(diffApplyFunction(_F2

\
|
ApplyFunction(y),y),y)=_c[1] _F2ApplyFunction(y)}]|
/

No solution appears when the differential equation is expressed in standard form, but when exp(x + y) is converted to

exp(1)^(x + y) the correct solution appears.

﻿