Internal problem ID [9837]
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]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }=3-\frac {1}{x^{2}}+2 \ln \left (x \right )} \]
✓ 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: 0.606 (sec). Leaf size: 258
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]
\[ y(x)\to \frac {1}{225} \left (-3 (17+75 c_2) \arctan (x)-\frac {51 x}{x^2+1}-\frac {34 x}{\left (x^2+1\right )^2}-\frac {225 c_2 x}{x^2+1}-\frac {150 c_2 x}{\left (x^2+1\right )^2}-\frac {225 c_1}{4 \left (x^2+1\right )^2}-9 x+\frac {47}{x-i}+\frac {47}{x+i}+45 x \log (x)+60 i \log (-x+i)+\frac {171}{2} i \log (1-i x)-\frac {171}{2} i \log (1+i x)+\frac {30 \log (x)}{x-i}+\frac {30 \log (x)}{x+i}-\frac {30 i \log (x)}{(x-i)^2}+\frac {30 i \log (x)}{(x+i)^2}-60 i \log (x+i)+\frac {75 c_2}{x-i}+\frac {75 c_2}{x+i}+\frac {225}{2} i c_2 \log (1-i x)-\frac {225}{2} i c_2 \log (1+i x)\right )+c_3 \]