4.2194   x3y′′′(x)+ x2log(x)y′′(x)+ 2xy′(x)− y(x) = 2x3

ODE

x3y′′′(x)+ x2 log(x)y′′(x) +2xy ′(x)− y(x) = 2x3

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

{                 (   ∫                                                                                          (                     )     (               )                           (             )       ) }
        x2 − (ln(x2))2        √- 1∕2(ln(x))2 (    (   √ -         ) 1∕2      (   √-           )  2) √ --−1∕2(ln(x))2−5∕2       3i 2√ -√--− 12   -         -i√-               (  3√-√ --−
 y (x) = 3 e        − 3  ix 2e         xErf  i∕2  2(ln(x)− 2)  e  − Erf  i∕2 2 (− 1+ ln(x)) e    πe        e    dx+   − 2 x  2 πe   + 3 C2  Erf  2  2(− 1+ ln (x))  +  ix  2  πe  + 3 C3  Erf  2  2(ln(x)

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*De
rivative[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)*(l
n(x)-2))+3*_C1)*x^2