ODE No. 1511

\[ x^3 y^{(3)}(x)+(x+8) x^3-6 (x-1) x^3 \log (x)+3 x^2 y''(x)-2 x y'(x)+2 y(x)=0 \] Mathematica : cpu = 0.0451298 (sec), leaf count = 51

DSolve[x^3*(8 + x) - 6*(-1 + x)*x^3*Log[x] + 2*y[x] - 2*x*Derivative[1][y][x] + 3*x^2*Derivative[2][y][x] + x^3*Derivative[3][y][x] == 0,y[x],x]
 

\[\left \{\left \{y(x)\to \frac {c_1}{x^2}+\frac {1}{450} \left (-50 x^4+50 x^4 \log (x)-18 x^3-135 x^3 \log (x)\right )+c_2 x+c_3 x \log (x)\right \}\right \}\] Maple : cpu = 0.034 (sec), leaf count = 49

dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*x^2*diff(diff(y(x),x),x)-2*x*diff(y(x),x)+2*y(x)-6*x^3*(x-1)*ln(x)+x^3*(x+8)=0,y(x))
 

\[y \left (x \right ) = \frac {\left (50 x^{6}-135 x^{5}+450 x^{3} c_{3}\right ) \ln \left (x \right )-50 x^{6}-18 x^{5}+450 c_{1} x^{3}+450 c_{2}}{450 x^{2}}\]