#20 page 751

> restart;

> y1:=x->x^3*exp(-3*x^(2/3)/4);

> x^(1/3)*diff(y1(x),x,x)+diff(y1(x),x)+(1/4*x^(-1/3)-1/(6*x)-6*x^(-5/3))*y1(x)=0;

> simplify(%);

> y2:=x->x^3*exp(-3*x^(2/3)/4)*v(x);

> x^(1/3)*diff(y2(x),x,x)+diff(y2(x),x)+(1/4*x^(-1/3)-1/(6*x)-6*x^(-5/3))*y2(x)=0;

> simplify(%);

> exp(-3/4*x^(2/3))*x^(7/3)*(6*z(x)+x*diff(z(x),x)) = 0;

>

> solve(%,diff(z(x),x));

> int(-1/z,z)=int(6/x,x);

> solve(%,z);

> int(%,x);

> %*x^3*exp(-3*x^(2/3)/4);

> y2:=unapply(%,x);

> x^(1/3)*diff(y2(x),x,x)+diff(y2(x),x)+(1/4*x^(-1/3)-1/(6*x)-6*x^(-5/3))*y2(x)=0;

> simplify(%);