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Question: why ODESteps(ode) unable to solve this first order quadrature ode?

Question:why ODESteps(ode) unable to solve this first order quadrature ode?

nm 9914
step-by-step differential-equations student odesteps
May 24 2024
1

This ode can be solved by just looking at it

ode:=(x+y(x))*diff(y(x),x)=0;

We see the solution is y=-x and y=c__1 because either (x+y)=0 or y'=0

But for some reason ODESteps(ode) says it cannot compute integral.

Any idea why?


 

26348

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

ode:=(x+y(x))*diff(y(x),x)=0;
Student:-ODEs:-ODESteps(ode);

ode := (x+y(x))*(diff(y(x), x)) = 0

"[[,,"Let's solve"],[,,(x+y(x)) ((ⅆ)/(ⅆx) y(x))=0],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Integrate both sides with respect to" x],[,,∫(x+y(x)) ((ⅆ)/(ⅆx) y(x)) ⅆx=∫0 ⅆx+`c__1`],["•",,"Cannot compute integral"],[,,∫(x+y(x)) ((ⅆ)/(ⅆx) y(x)) ⅆx=`c__1`]]"

> 

 


 

Download odestep_quadrature_unable_to_solve_maple_2024.mw

update:

Here is another simpler example that also confused it
 

26348

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

ode:=x*diff(y(x),x)=0;
Student:-ODEs:-ODESteps(ode);

ode := x*(diff(y(x), x)) = 0

"[[,,"Let's solve"],[,,x ((ⅆ)/(ⅆx) y(x))=0],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Integrate both sides with respect to" x],[,,∫x ((ⅆ)/(ⅆx) y(x)) ⅆx=∫0 ⅆx+`c__1`],["•",,"Cannot compute integral"],[,,∫x ((ⅆ)/(ⅆx) y(x)) ⅆx=`c__1`]]"

> 

 

> 

 


 

Download odestep_quadrature_unable_to_solve_v2_maple_2024.mw

update

Here is another one which it gets wrong. 
 

26348

> 

interface(version);

`Standard Worksheet Interface, Maple 2024.0, Windows 10, March 01 2024 Build ID 1794891`

> 

ode:=y(x)*diff(y(x),x)=0;
Student:-ODEs:-ODESteps(ode);

ode := y(x)*(diff(y(x), x)) = 0

"[[,,"Let's solve"],[,,y(x) ((ⅆ)/(ⅆx) y(x))=0],["•",,"Highest derivative means the order of the ODE is" 1],[,,(ⅆ)/(ⅆx) y(x)],["•",,"Integrate both sides with respect to" x],[,,∫y(x) ((ⅆ)/(ⅆx) y(x)) ⅆx=∫0 ⅆx+`c__1`],["•",,"Evaluate integral"],[,,((y(x))^2)/2=`c__1`],["•",,"Solve for" y(x)],[,,{y(x)=sqrt(2) sqrt(`c__1`),y(x)=-sqrt(2) sqrt(`c__1`)}]]"

> 

dsolve(ode);

y(x) = 0, y(x) = -c__1

> 

 


The correct solution is given by dsolve, which is y=0 and y=constant (I do not know why dsolve put minus sign in front of the constant, but it is still correct).

Download odestep_quadrature_unable_to_solve_v3_maple_2024.mw

 

 
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