✓ Maple : cpu = 0.01 (sec), leaf count = 27
Let
And
Hence the original ODE becomes
This is standard second order with constant coefficients. The solution is
Substituting back
Verification
restart; ode:=diff(diff(y(x),x),x)+diff(y(x),x)+a*exp(-2*x)*y(x)=0; ys:=_C1*cos(sqrt(a)*exp(-x))+_C2*sin(sqrt(a)*exp(-x)); odetest(y(x)=ys,ode); 0