59.1.480 problem 496

Internal problem ID [9652]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 496
Date solved : Monday, January 27, 2025 at 06:05:03 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.020 (sec). Leaf size: 73

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

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

✓ Solution by Mathematica

Time used: 0.261 (sec). Leaf size: 62

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

\[ y(x)\to e^{-\frac {1}{2} (x-6) x} \left (x^2-6 x+8\right ) \left (c_2 \int _1^x\frac {e^{\frac {1}{2} (K[1]-6) K[1]}}{(K[1]-4)^2 (K[1]-2)^2}dK[1]+c_1\right ) \]