78.8.16 problem 16

Internal problem ID [18214]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Miscellaneous Problems for Chapter 2. Problems at page 99
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 11:39:12 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }&=1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 16

dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)=1,y(x), singsol=all)
 

\[ y = c_{1} \ln \left (x \right )+\frac {\ln \left (x \right )^{2}}{2}+c_{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 21

DSolve[x^2*D[y[x],{x,2}]+x*D[y[x],x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log ^2(x)}{2}+c_1 \log (x)+c_2 \]