59.1.324 problem 331

Internal problem ID [9496]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 331
Date solved : Monday, January 27, 2025 at 06:03:27 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }+\left (x -6\right ) y^{\prime }-3 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 39

dsolve(x*diff(y(x),x$2)+(x-6)*diff(y(x),x)-3*y(x)=0,y(x), singsol=all)
 

\[ y = c_{1} \left (x^{3}-12 x^{2}+60 x -120\right )+c_{2} {\mathrm e}^{-x} \left (x^{3}+12 x^{2}+60 x +120\right ) \]

✓ Solution by Mathematica

Time used: 0.078 (sec). Leaf size: 98

DSolve[x*D[y[x],{x,2}]+(x-6)*D[y[x],x]-3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {2 e^{-x/2} \sqrt {x} \left (\left (c_1 x^3+12 i c_2 x^2+60 c_1 x+120 i c_2\right ) \cosh \left (\frac {x}{2}\right )-\left (12 c_1 \left (x^2+10\right )+i c_2 x \left (x^2+60\right )\right ) \sinh \left (\frac {x}{2}\right )\right )}{\sqrt {\pi } \sqrt {-i x}} \]