78.8.23 problem 23

Internal problem ID [18221]
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 : 23
Date solved : Tuesday, January 28, 2025 at 11:40:39 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime }+x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 10

dsolve((1+x^2)*diff(y(x),x$2)+x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = c_{1} +\operatorname {arcsinh}\left (x \right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 13

DSolve[(1+x^2)*D[y[x],{x,2}]+x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \text {arcsinh}(x)+c_2 \]