40.13.13 problem 33

Internal problem ID [6767]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 18. Linear equations with variable coefficients (Equations of second order). Supplemetary problems. Page 120
Problem number : 33
Date solved : Monday, January 27, 2025 at 02:29:53 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x y^{\prime \prime }-3 y^{\prime }+\frac {3 y}{x}&=x +2 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \frac {\left (c_1 \,x^{2}-2 x -2 \ln \left (x \right )+2 c_2 \right ) x}{2} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 30

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

\[ y(x)\to \frac {1}{2} x \left (2 c_2 x^2-2 x-2 \log (x)-3+2 c_1\right ) \]