nm

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These are questions asked by nm

Why when given IC for this ode, where the IC do not really makes much sense, so was not used. But the question is on the format of the output of the Maple dsolve. It gives solution as [{y(t) = c__1}]  instead of y(t) = c__1
 

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

restart;

ode:=diff(y(t),t)=0;
IC:=y(0)=t;
sol:=dsolve(ode)

diff(y(t), t) = 0

y(0) = t

y(t) = c__1

sol:=dsolve([ode,IC])

[{y(t) = c__1}]


 

Related question. Since Maple did not use the IC, should there have been warning message generated that IC was ignored?

 

Download strange_format_of_solution_sept_19_2025.mw

 

 

Any idea why Maple dsolve can't find solution to this ode? From textbook

The strange thing, it solves if it asked for implicit solution. But the default, will give no solution.

Is this a defect? Should it not have returned the book solution automatically?   How is a user supposed to know the ode has a solution or not, if default call returns no solution?

restart;

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1877 and is the same as the version installed in this computer, created 2025, July 11, 19:24 hours Pacific Time.`

restart;

ode:=v(x)*diff(v(x),x) = g;
ic:=v(x__0) = v__0;
sol:=dsolve([ode,ic]);

v(x)*(diff(v(x), x)) = g

v(x__0) = v__0

restart;

ode:=v(x)*diff(v(x),x) = g;
ic:=v(x__0) = v__0;
sol:=dsolve([ode,ic],'implicit');

v(x)*(diff(v(x), x)) = g

v(x__0) = v__0

-2*g*x+v(x)^2+2*g*x__0-v__0^2 = 0

#why did not default call return this?
PDEtools:-Solve(sol,v(x))

v(x) = (2*g*x-2*g*x__0+v__0^2)^(1/2), v(x) = -(2*g*x-2*g*x__0+v__0^2)^(1/2)

Download dsolve_gives_no_solution_sept_2_2025.mw

I was surprised that Maple can't solve this first order ode which is exact ode.

I solved by hand and Maple says my solution is correct.

Any one can find why Maple failed to solve this and if older versions can solve it? Also tried implicit option, but that did not help.

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

SupportTools:-Version();

`The Customer Support Updates version in the MapleCloud is 29 and is the same as the version installed in this computer, created June 23, 2025, 10:25 hours Eastern Time.`

restart;

ode:=diff(y(x),x) = (2*sin(2*x)-tan(y(x)))/x/sec(y(x))^2;

diff(y(x), x) = (2*sin(2*x)-tan(y(x)))/(x*sec(y(x))^2)

sol:=dsolve(ode);

mysol:=cos(2*x)+x*tan(y(x))=c__1;

cos(2*x)+x*tan(y(x)) = c__1

odetest(mysol,ode);

0

 

 

Download maple_solving_exact_ode_august_25_2025.mw

THis is problem from textbook. Maple do not give solution. 

But when asked for implicit solution, it gives one.  Should it not have done this automatically?

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

ode:=y(x)*diff(y(x),x) = a;
ic:=y(0) = b;
sol:=dsolve([ode,ic]);

y(x)*(diff(y(x), x)) = a

y(0) = b

sol:=dsolve([ode,ic],'implicit')

-2*a*x+y(x)^2-b^2 = 0

 

 

Download why_no_solution_maple_2025_1.mw

We see now there are two solutions for y(x), since quadratic.

So why dsolve do not solve this and at least give implicit solution automatically? Should this be reported as defect?

Any idea why Maple simplifies 1+sin(x)^2 to 2-cos(x)^2?  Leaf count is larger also.

interface(version);

`Standard Worksheet Interface, Maple 2025.1, Linux, June 12 2025 Build ID 1932578`

e1:=1+sin(x)^2;

1+sin(x)^2

e2:=simplify(e1)

-cos(x)^2+2

MmaTranslator:-Mma:-LeafCount(e1)

6

MmaTranslator:-Mma:-LeafCount(e2)

8

 

 

Download strange_simplification_august_20_2025.mw

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