Trying to obtain an explicit solution of a second order ODE
- Subject: Trying to obtain an explicit solution of a second order ODE
- From: Aleksas Domarkas
- Date: Wed, 17 Apr 2013 15:20:49 +0300
see
http://www.math.utexas.edu/pipermail/maxima/2013/032582.html
(%i1) assume(C>0);
de: 'diff(y,x,2)=-C*'diff(y,x)^2/y;
(%o1) [C>0]
(%o2) 'diff(y,x,2)=-(('diff(y,x,1))^2*C)/y
(%i3) ode2(de,y,x);
(%o3) (y*%e^(log(y)*C))/(%k1*C+%k1)=x+%k2
(%i4) radcan(%);
(%o4) y^(C+1)/(%k1*C+%k1)=x+%k2
(%i5) solve(%,y);
"Is "C" an "integer"?"n;
"Is "%k1*(x+%k2)" positive, negative, or zero?"p;
(%o5) [y=(%k1*x*C+%k1*%k2*C+%k1*x+%k1*%k2)^(1/(C+1))]
Solution:
(%i6) sol:factor(%)[1];
(%o6) y=(%k1*(x+%k2))^(1/(C+1))*(C+1)^(1/(C+1))
Test:
(%i7) subst(sol,de)$
(%i8) ev(%, nouns)$
(%i9) ratsimp(lhs(%)-rhs(%));
(%o9) 0
regards
Aleksas D