ODE
\[ x^2 (y(x)+3) y'''(x)-3 (x+2) x y''(x)+6 (x+1) y'(x)-6 y(x)=0 \] ODE Classification
[NONE]
Book solution method
TO DO
Mathematica ✗
cpu = 0.224527 (sec), leaf count = 0 , could not solve
DSolve[-6*y[x] + 6*(1 + x)*Derivative[1][y][x] - 3*x*(2 + x)*Derivative[2][y][x] + x^2*(3 + y[x])*Derivative[3][y][x] == 0, y[x], x]
Maple ✓
cpu = 0.946 (sec), leaf count = 76
\[ \left \{ y \left ( x \right ) ={\it ODESolStruc} \left ( {\it \_b} \left ( {\it \_a} \right ) ,[ \left \{ \left ( 3+{\it \_b} \left ( {\it \_a} \right ) \right ) {\frac {{\rm d}^{2}}{{\rm d}{{\it \_a}}^{2}}}{\it \_b} \left ( {\it \_a} \right ) -{\frac {{\it \_a}\, \left ( {\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) \right ) ^{2}+6\,{\it \_a}\,{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -2\,{\it \_C1}\,{\it \_a}+12\,{\frac {\rm d}{{\rm d}{\it \_a}}}{\it \_b} \left ( {\it \_a} \right ) -12\,{\it \_b} \left ( {\it \_a} \right ) }{2\,{\it \_a}}}=0 \right \} , \left \{ {\it \_a}=x,{\it \_b} \left ( {\it \_a} \right ) =y \left ( x \right ) \right \} , \left \{ x={\it \_a},y \left ( x \right ) ={\it \_b} \left ( {\it \_a} \right ) \right \} ] \right ) \right \} \] Mathematica raw input
DSolve[-6*y[x] + 6*(1 + x)*y'[x] - 3*x*(2 + x)*y''[x] + x^2*(3 + y[x])*y'''[x] == 0,y[x],x]
Mathematica raw output
DSolve[-6*y[x] + 6*(1 + x)*Derivative[1][y][x] - 3*x*(2 + x)*Derivative[2][y][x] + x^2*(3 + y[x])*Derivative[3][y][x] == 0, y[x], x]
Maple raw input
dsolve(x^2*(3+y(x))*diff(diff(diff(y(x),x),x),x)-3*x*(2+x)*diff(diff(y(x),x),x)+6*(1+x)*diff(y(x),x)-6*y(x) = 0, y(x),'implicit')
Maple raw output
y(x) = ODESolStruc(_b(_a),[{(3+_b(_a))*diff(diff(_b(_a),_a),_a)-1/2*(_a*diff(_b(_a),_a)^2+6*_a*diff(_b(_a),_a)-2*_C1*_a+12*diff(_b(_a),_a)-12*_b(_a))/_a = 0}, {_a = x, _b(_a) = y(x)}, {x = _a, y(x) = _b(_a)}])