Internal problem ID [9085]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1506.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _fully, _exact, _linear]]
Solve \begin {gather*} \boxed {4 x^{2} y^{\prime \prime \prime }+\left (x^{2}+14 x -1\right ) y^{\prime \prime }+4 \left (x +1\right ) y^{\prime }+2 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(4*x^2*diff(diff(diff(y(x),x),x),x)+(x^2+14*x-1)*diff(diff(y(x),x),x)+4*(x+1)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \left (c_{3}+\int \frac {\left (2 c_{1} x +c_{2}\right ) {\mathrm e}^{\frac {x}{4}} {\mathrm e}^{\frac {1}{4 x}}}{4 x^{\frac {5}{2}}}d x \right ) {\mathrm e}^{-\frac {x}{4}} {\mathrm e}^{-\frac {1}{4 x}} \sqrt {x} \]
✓ Solution by Mathematica
Time used: 0.189 (sec). Leaf size: 126
DSolve[2*y[x] + 4*(1 + x)*y'[x] + (-1 + 14*x + x^2)*y''[x] + 4*x^2*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-\frac {(x+1)^2}{4 x}} \sqrt {x} \left (\sqrt {e} c_2 \int _1^x\frac {e^{\frac {K[1]^2+1}{4 K[1]}}}{K[1]^{5/2}}dK[1]-\sqrt {\pi } c_3 \left (e \text {Erfi}\left (\frac {1-x}{2 \sqrt {x}}\right )+\text {Erfi}\left (\frac {x+1}{2 \sqrt {x}}\right )\right )+\sqrt {e} c_1+i (e-1) \sqrt {\pi } c_3\right ) \\ \end{align*}