2.1517   ODE No. 1517

\[ x^3 y^{(3)}(x)-2 x^3+x^2 y''(x)+2 x y'(x)-y(x)+\log (x)=0 \] Mathematica : cpu = 0.378475 (sec), leaf count = 601

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

\[\left \{\left \{y(x)\to \frac {i \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]\right ) \left (\frac {2 x^3}{3-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]}+\frac {\log (x)}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]}+\frac {1}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]^2}\right )}{\sqrt {23}}-\frac {i \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) \left (\frac {2 x^3}{3-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}+\frac {\log (x)}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}+\frac {1}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]^2}\right )}{\sqrt {23}}+\frac {i \left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]-\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]\right ) x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-2} \left (\frac {2 x^3}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]+1}-\frac {\log (x)}{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-2}+\frac {1}{\left (\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]+\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]-2\right )^2}\right )}{\sqrt {23}}+c_1 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,1\right ]}+c_3 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,3\right ]}+c_2 x^{\text {Root}\left [\text {$\#$1}^3-2 \text {$\#$1}^2+3 \text {$\#$1}-1\& ,2\right ]}\right \}\right \}\] Maple : cpu = 0.419 (sec), leaf count = 866

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=0,y(x))
 

\[\text {Expression too large to display}\]