60.4.38 problem 1486

Internal problem ID [11489]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1486
Date solved : Tuesday, January 28, 2025 at 06:06:36 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime \prime }-8 x y^{\prime }+8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 50

dsolve((2*x-1)*diff(diff(diff(y(x),x),x),x)-8*x*diff(y(x),x)+8*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} x +{\mathrm e}^{2 x} c_{2} -\frac {c_3 x \,{\mathrm e}^{-1} \operatorname {Ei}_{1}\left (-1+2 x \right )}{2}+\frac {c_3 \,\operatorname {Ei}_{1}\left (4 x -2\right ) {\mathrm e}^{2 x -2}}{4}+\frac {c_3 \,{\mathrm e}^{-2 x}}{4} \]

✓ Solution by Mathematica

Time used: 0.167 (sec). Leaf size: 144

DSolve[8*y[x] - 8*x*D[y[x],x] + (-1 + 2*x)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x \left (c_2 \int _1^x\frac {\exp \left (\int _1^{K[3]}\left (\frac {2}{2 K[1]-1}+2-\frac {1}{2 K[1]}\right )dK[1]\right )}{K[3]^{3/2}}dK[3]+c_3 \int _1^x\frac {\exp \left (\int _1^{K[4]}\left (\frac {2}{2 K[1]-1}+2-\frac {1}{2 K[1]}\right )dK[1]\right ) \int _1^{K[4]}\exp \left (-2 \int _1^{K[2]}\left (\frac {2}{2 K[1]-1}+2-\frac {1}{2 K[1]}\right )dK[1]\right )dK[2]}{K[4]^{3/2}}dK[4]+c_1\right ) \]