'1.8*a+.4000000000*b+103.9*c-.5000000000*e-102.6*g = 0', '.5000000000*b+102.6*c+.3*d+.3500000000*e-102.1*g = 0', '-.3*a-.3500000000*b+102.1*c+2.5*d-1.450000000*e-102.6*g = 0', '-2.5*a+1.450000000*b+102.6*c+3.3*d+1.050000000*e-102.4*g = 0', '-3.3*a-1.050000000*b+102.4*c+.7*d+.2500000000*e-105.1*g = 0', '-.7*a-.2500000000*b+105.1*c-.2*d+.2000000000*e-105.7*g = 0'

i use solve, it return a = a 

int(y^2/2 - lambda*(u*diff(y,t)-diff(u,t)-a), t);

with(Physics):

diff(y(t)^2/2 - lambda(t)*(u(t)*diff(y(t),t)-diff(u(t),t)-a), u(t)); # u -> something

diff(lambda(t),t) disappear

should be

diff(lambda(t),t)+Physics[`*`](lambda(t), diff(y(t), t))

diff(y(t)^2/2 - lambda(t)*(u(t)*diff(y(t),t)-diff(u(t),t)-a), y(t)); # y -> something

u*diff(lambda(t...

x0 := 3*u+2*v+w-10;

x1 := 4*u+3*v+w-12;

c := -x2^3+x1^3+x0*x1^2;

subs(x0 = a1*u+a2*v, subs(x1 = a3*u+a4*v, subs(x2 = a5*u+a6*v, c)))

match(-x2^3+x1^3+x0*x1^2 = -(a5*u+a6*v)^3+(a3*u+a4*v)^3+(a1*u+a2*v)*(a3*u+a4*v)^2, {x0, x1, x2}, 's');

how to find a1,a2,...a6

with(algcurves):

f := y^2 - x^3  - x^2 =0;

c := simplify(subs(x=x1/x0, subs(y=x2/x0, f)));

c := -x2^3+x1^3+x0*x1^2;

parametrization(c, x0, x1, x2, u, v);

how to make

x0 = a0*u + b0*v

x1 = a1*u + b1*v

x2 = a2*u + b2*v