(%i1) | kill(all)$ |
ode : part4,intro: ricatti
[email protected],04/02/2017
Theory Ricatti : ODE (reaction kinetics)
(dy/dx) = p(x)*y^2+q(x)*y+r(x)
(%i1) |
load('contrib_ode)$ |
(%i2) | depends([y,p,q,r],[x]); |
(%i6) |
eq1:'diff(y,x)=p(x)*y^2+q(x)*y+r(x); eq2:subst(p(x)=p(x),eq1); eq3:contrib_ode(eq2,y,x)[1]; method; |
(%i8) |
eq4:part(eq3,1); eq5:part(eq3,2); |
eq4 : What subst. to use → linear second order
equation with nonconstant coefficients.
check solution : same as eq5
(%i9) | dependencies; |
(%i10) | depends([%u],x); |
(%i11) | dependencies; |
(%i12) | eq6:subst(eq4,eq2); |
(%i13) | eq7:ev(part(eq6,1),nouns)=ev(part(eq6,2),nouns); |
(%i14) | eq8:radcan(eq7)*%u; |
(%i15) | eq9:lhs(eq8)-rhs(eq8)=0; |
(%i16) |
ratsimp((%u*('diff(%u,x,2))-('diff(%u,x,1))^2)/%u- (%u^2*r(x)+%u*('diff(%u,x,1))*q(x)-('diff(%u,x,1))^2)/%u)=0; |