59.1.437 problem 450

Internal problem ID [9609]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 450
Date solved : Monday, January 27, 2025 at 06:04:37 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 16

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

\[ y = {\mathrm e}^{x} c_{1} +c_{2} x \,{\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.350 (sec). Leaf size: 69

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

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