62.32.1 problem Ex 1

Internal problem ID [12978]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VIII, Linear differential equations of the second order. Article 55. Summary. Page 129
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:46:10 AM
CAS classification : [_Laguerre]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{x} c_{1} +c_{2} \left (x^{3}+3 x^{2}+6 x +6\right ) \]

✓ Solution by Mathematica

Time used: 0.427 (sec). Leaf size: 78

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

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