Internal problem ID [9080]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1503.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 y^{\prime \prime } x +10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 86
dsolve((x^2+1)*diff(diff(diff(y(x),x),x),x)+8*x*diff(diff(y(x),x),x)+10*diff(y(x),x)-3+1/x^2-2*ln(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+2\right ) x^{2} c_{1}}{\left (x^{2}+1\right )^{2}}+\frac {x \left (x^{2}+3\right ) c_{2}}{\left (x^{2}+1\right )^{2}}+\frac {c_{3}}{\left (x^{2}+1\right )^{2}}+\frac {x \left (45 \ln \left (x \right ) x^{4}-9 x^{4}+150 \ln \left (x \right ) x^{2}-50 x^{2}+225 \ln \left (x \right )-225\right )}{225 \left (x^{2}+1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 129
DSolve[-3 + x^(-2) - 2*Log[x] + 10*y'[x] + 8*x*y''[x] + (1 + x^2)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {480 \left (x^2+1\right )^2 \arctan (x)-36 x^5+100 x^3-300 c_2 x^3+240 i \left (x^2+1\right )^2 \log (-x+i)+900 c_3 \left (x^2+1\right )^2+60 x \left (\left (3 x^4+10 x^2+15\right ) \log (x)-4 i x \left (x^2+2\right ) \log (x+i)\right )-240 i \log (x+i)-900 c_2 x-225 c_1}{900 \left (x^2+1\right )^2} \\ \end{align*}