ODE
\[ x^3 y'''(x)+x^2 \log (x) y''(x)+2 x y'(x)-y(x)=2 x^3 \] ODE Classification
[[_3rd_order, _linear, _nonhomogeneous]]
Book solution method
TO DO
Mathematica ✗
cpu = 0.0143274 (sec), leaf count = 0 , could not solve
DSolve[-y[x] + 2*x*Derivative[1][y][x] + x^2*Log[x]*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 2*x^3, y[x], x]
Maple ✓
cpu = 0.365 (sec), leaf count = 141
\[ \left \{ y \left ( x \right ) ={\frac {{x}^{2}}{3}{{\rm e}^{-{\frac { \left ( \ln \left ( x \right ) \right ) ^{2}}{2}}}} \left ( -3\,\int \!ix\sqrt {2}{{\rm e}^{1/2\, \left ( \ln \left ( x \right ) \right ) ^{2}}} \left ( x{\it Erf} \left ( i/2\sqrt {2} \left ( \ln \left ( x \right ) -2 \right ) \right ) {{\rm e}^{1/2}}-{\it Erf} \left ( i/2\sqrt {2} \left ( -1+\ln \left ( x \right ) \right ) \right ) {{\rm e}^{2}} \right ) \sqrt {\pi }{{\rm e}^{-1/2\, \left ( \ln \left ( x \right ) \right ) ^{2}}}{{\rm e}^{-5/2}}\,{\rm d}x+ \left ( -{\frac {3\,i}{2}}{x}^{2}\sqrt {2}\sqrt {\pi }{{\rm e}^{-{\frac {1}{2}}}}+3\,{\it \_C2} \right ) {\it Erf} \left ( {\frac {i}{2}}\sqrt {2} \left ( -1+\ln \left ( x \right ) \right ) \right ) + \left ( i{x}^{3}\sqrt {2}\sqrt {\pi }{{\rm e}^{-2}}+3\,{\it \_C3} \right ) {\it Erf} \left ( {\frac {i}{2}}\sqrt {2} \left ( \ln \left ( x \right ) -2 \right ) \right ) +3\,{\it \_C1} \right ) } \right \} \] Mathematica raw input
DSolve[-y[x] + 2*x*y'[x] + x^2*Log[x]*y''[x] + x^3*y'''[x] == 2*x^3,y[x],x]
Mathematica raw output
DSolve[-y[x] + 2*x*Derivative[1][y][x] + x^2*Log[x]*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 2*x^3, y[x], x]
Maple raw input
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+x^2*diff(diff(y(x),x),x)*ln(x)+2*x*diff(y(x),x)-y(x) = 2*x^3, y(x),'implicit')
Maple raw output
y(x) = 1/3*exp(-1/2*ln(x)^2)*(-3*Int(I*x*2^(1/2)*exp(1/2*ln(x)^2)*(x*erf(1/2*I*2^(1/2)*(ln(x)-2))*exp(1/2)-erf(1/2*I*2^(1/2)*(-1+ln(x)))*exp(2))*Pi^(1/2)*exp(-1/2*ln(x)^2)*exp(-5/2),x)+(-3/2*I*x^2*2^(1/2)*Pi^(1/2)*exp(-1/2)+3*_C2)*erf(1/2*I*2^(1/2)*(-1+ln(x)))+(I*x^3*2^(1/2)*Pi^(1/2)*exp(-2)+3*_C3)*erf(1/2*I*2^(1/2)*(ln(x)-2))+3*_C1)*x^2