83.36.2 problem 2

Internal problem ID [19436]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VIII. Linear equations of second order. Excercise VIII (A) at page 125
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 01:42:52 PM
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)
 

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 29

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

\[ y(x)\to c_1 e^x-c_2 \left (x^3+3 x^2+6 x+6\right ) \]