I am trying to substitute the value of the first derivative in the equation with wxMaxima. The substitution steps works fine with simple algebra but it does not work with derivative. It also substitutes the second derivative but I want to see first derivative replaced only. Where I am doing wrong?
(%i5) kill(all);
(%o0) done
(%i5) eq1:diff(y(x),x)+(a*x+b*y(x))=0;
(eq1) 'diff(y(x),x,1)+b*y(x)+a*x=0
(%i6) eq2:diff(eq1,x);
(eq2) 'diff(y(x),x,2)+b*('diff(y(x),x,1))+a=0
(%i7) eq3:solve(eq1,diff(y(x),x));
(eq3) ['diff(y(x),x,1)=-b*y(x)-a*x]
(%i9) eq5:subst(eq3,eq4),derivsubst=true;
(eq5) ['diff((-(b*y(x)+a*x+c)/(%beta*y(x)+%alpha*x+%gamma)),x,1)=-(-(((%alpha*b-%beta*a)*x-%beta*c+%gamma*b)*(b*y(x)+a*x+c)/(%beta*y(x)+%alpha*x+%gamma)+ (%beta*a-%alpha*b)*y(x)-%alpha*c+%gamma*a)/(%beta^2*y(x)^2(2*%alpha*%beta*x+2*%gamma*%beta)*y(x)+%alpha^2*x^2+2*%gamma*%alpha*x+%gamma^2)]('diff(y(x),x,1))+a=0)
(%i5) test:a-2*v=v+2-a;
(test) a-2*v=v-a+2
(%i6) test2:solve(test,a);
(test2) [a=(3*v+2)/2]
(%i7) subst([test2], a+b);
(%o7) (3*v+2)/2+b
