Advanced Search

Question: why dsolve gives this extra solution?

Question:why dsolve gives this extra solution?

nm 10189 Maple 2024
ode dsolve differential-equations
June 05 2024
1

We see that this ode (x + y(x))*(1+diff(y(x),x)) = 0  has 2 solutions, One when (x + y(x))=0 and one when (1+diff(y(x),x))=0. Maple gives 3 solutions. They are correct but why?

Also when changing (1+diff(y(x),x)) to (a+diff(y(x),x)) now it gives only two solution.

Why does this happen? Should it not just return 2 solutions in both cases? and more strange one

(x + y(x))^2 *(1+diff(y(x), x))=0; now it gives 4 solutions. But this is no different. We also have 2 solutions. One when (x + y(x))=0 and one when (1+diff(y(x), x))=0. This time the extra two solutions are complex. 

17168

> 

interface(version);

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

> 

Physics:-Version();

`The "Physics Updates" version in the MapleCloud is 1754 and is the same as the version installed in this computer, created 2024, June 3, 20:39 hours Pacific Time.`

> 

ode:=(x + y(x))*(a+diff(y(x),x)) = 0;
dsolve(ode);
map(X->odetest(X,ode),[%])

(x+y(x))*(a+diff(y(x), x)) = 0

y(x) = -x, y(x) = -a*x+c__1

[0, 0]

> 

ode:=(x + y(x))*(1+diff(y(x),x)) = 0;
dsolve(ode);
map(X->odetest(X,ode),[%])

(x+y(x))*(1+diff(y(x), x)) = 0

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

[0, 0, 0]

> 

ode:= (x + y(x))^2 *(1+diff(y(x), x))=0;
dsolve(ode);
map(X->odetest(X,ode),[%])
> 

 

(x+y(x))^2*(1+diff(y(x), x)) = 0

y(x) = -x, y(x) = -x+c__1, y(x) = -(1/2)*c__1-((1/2)*I)*3^(1/2)*c__1-x, y(x) = -(1/2)*c__1+((1/2)*I)*3^(1/2)*c__1-x

[0, 0, 0, 0]

 

 

Download why_extra_solution_from_dsolve_june_5_2024.mw
Please Wait...