Internal problem ID [9096]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1517.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime } x^{3}+x^{2} y^{\prime \prime }+\ln \relax (x )+2 y^{\prime } x -y-2 x^{3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 1770
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), singsol=all)
\[ \text {Expression too large to display} \]
✓ Solution by Mathematica
Time used: 0.372 (sec). Leaf size: 91
DSolve[-2*x^3 + Log[x] - y[x] + 2*x*y'[x] + x^2*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 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 ]}+\frac {2 x^3}{17}+\log (x)+3 \\ \end{align*}