60.4.39 problem 1487

Internal problem ID [11490]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1487
Date solved : Monday, January 27, 2025 at 11:22:38 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime \prime }+\left (x +4\right ) y^{\prime \prime }+2 y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 38

dsolve((2*x-1)*diff(diff(diff(y(x),x),x),x)+(x+4)*diff(diff(y(x),x),x)+2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (c_3 +\int \frac {\left (2 c_{1} x +c_{2} \right ) {\mathrm e}^{\frac {x}{2}}}{\left (-1+2 x \right )^{{3}/{4}}}d x \right ) {\mathrm e}^{-\frac {x}{2}}}{\left (-1+2 x \right )^{{1}/{4}}} \]

✓ Solution by Mathematica

Time used: 60.472 (sec). Leaf size: 66

DSolve[2*D[y[x],x] + (4 + x)*D[y[x],{x,2}] + (-1 + 2*x)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^xe^{-\frac {K[1]}{2}} \left (\frac {2 \sqrt {2} c_1 K[1]}{(2 K[1]-1)^{5/4}}+c_2 L_{-\frac {1}{4}}^{\frac {5}{4}}\left (\frac {K[1]}{2}-\frac {1}{4}\right )\right )dK[1]+c_3 \]