59.1.688 problem 705

Internal problem ID [9860]
Book : Collection of Kovacic problems
Section : section 1
Problem number : 705
Date solved : Monday, January 27, 2025 at 06:15:08 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+\left (x^{2}+x \right ) y^{\prime }+\left (x -9\right ) y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 38

dsolve(x^2*diff(y(x),x$2)+(x+x^2)*diff(y(x),x)+(x-9)*y(x)=0,y(x), singsol=all)
 

\[ y = \frac {c_{2} \left (x^{3}+9 x^{2}+36 x +60\right ) {\mathrm e}^{-x}+c_{1} \left (x^{2}-8 x +20\right )}{x^{3}} \]

✓ Solution by Mathematica

Time used: 0.501 (sec). Leaf size: 96

DSolve[x^2*D[y[x],{x,2}]+(x+x^2)*D[y[x],x]+(x-9)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\left (x^2-8 x+20\right ) \exp \left (\int _1^x\frac {K[1]-5}{2 K[1]}dK[1]-\frac {x}{2}\right ) \left (c_2 \int _1^x\frac {\exp \left (-2 \int _1^{K[2]}\frac {K[1]-5}{2 K[1]}dK[1]\right )}{\left (K[2]^2-8 K[2]+20\right )^2}dK[2]+c_1\right )}{\sqrt {x}} \]