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Re: [Maxima-discuss] solve identity
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From: David B. <dbm...@gm...> - 2025-06-10 05:27:31
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<p>On 10/06/2025 14:39, Aleksas Domarkas wrote:</p>
<blockquote type="cite"
cite="mid:CA+...@ma...">
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<div dir="ltr">In Maple
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<div>T:=3*a^2*x^(2*b)+(3*a*b-a)*x^b-3*x^(2/3)=0:</div>
<div>solve(identity(T,x,[a,b]);</div>
<div>return</div>
<div>[[a=-1,b=1/3],[a=1,b=1/3]]</div>
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<div>How to do it with Maxima ?</div>
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<div>I am looking solution y=a*x^b of Riccati eguation</div>
<div>3*x*'diff(y,x)=3*x^(2/3)+(1-3*y)*y;</div>
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</blockquote>
<p>You can solve it directly:</p>
<p><font face="monospace">(%i1)
eq:3*x*'diff(y,x)=3*x^(2/3)+(1-3*y)*y;<br>
dy 2/3<br>
(%o1) 3 x -- = (1 - 3 y) y + 3 x<br>
dx<br>
(%i2) load('contrib_ode);<br>
(%o2)
/usr/share/maxima/5.47.0/share/contrib/diffequations/contrib_ode.mac<br>
(%i3) contrib_ode(eq,y,x);<br>
1/3 1/3<br>
(%o3) [y = tanh(3 x + %c) x ]<br>
(%i4) ode_check(eq,%[1]);<br>
(%o4) 0<br>
(%i5) method;<br>
(%o5) riccati</font><br>
</p>
<p><span style="white-space: pre-wrap">You can print diagnostic messages and look at the source code and references for details</span></p>
<p><span style="white-space: pre-wrap"><font face="monospace">(%i6) put('contrib_ode,true,'verbose);
(%o6) true
(%i7) contrib_ode(eq,y,x);
-> ode_contrib
First order equation
-> ode2
in ode1_nonlinear
-> ode1_factor
in ode1_factor
2 2/3
cannot factor 3 y - y + 3 %p x - 3 x
-> ode1_clairaut
Expression not free of x and y:
2/3 2/3 2
3 (y + %r) + %p (- 3 y - 2 y - 3 %r)
- -------------------------------------------
2/3
%p
-> ode1_lagrange
In ode1_lagrange
-> ode1_riccati
is Ricatti equation
1
f0: ----
1/3
x
1
f1: ---
3 x
1
f2: - -
x
equation is special Riccati equation
-> In ode1_riccati_special
1
a: -
3
b: 1
c: 1
2
n: -
3
Case (a.i)
-> In ode1_riccati_special_i
1
a: -
3
b: 1
c: 1
2
n: -
3
Case (a.i.1) b*c>0, b>0 and c>0
1/3 1/3
(%o7) [y = tanh(3 x + %c) x ]
</font>
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