60.3.129 problem 1133

Internal problem ID [11139]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1133
Date solved : Monday, January 27, 2025 at 10:46:45 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -1\right ) y^{\prime \prime }-\left (3 x -4\right ) y^{\prime }+\left (x -3\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.122 (sec). Leaf size: 31

dsolve((2*x-1)*diff(diff(y(x),x),x)-(3*x-4)*diff(y(x),x)+(x-3)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {\sqrt {2}\, \left (\left (\frac {c_{1}}{4}+c_{2} \right ) \Gamma \left (-\frac {1}{4}, -\frac {1}{4}+\frac {x}{2}\right )+\Gamma \left (\frac {3}{4}\right ) c_{1} \right ) {\mathrm e}^{-\frac {1}{4}+x}}{2} \]

✓ Solution by Mathematica

Time used: 0.143 (sec). Leaf size: 93

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

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