78.7.7 problem 1 (g)

Internal problem ID [18193]
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. Section 11 (Reduction of order). Problems at page 87
Problem number : 1 (g)
Date solved : Tuesday, January 28, 2025 at 11:37:42 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+y^{\prime }&=4 x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(x*diff(y(x),x$2)+diff(y(x),x)=4*x,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 16

DSolve[x*D[y[x],{x,2}]+D[y[x],x]==4*x,y[x],x,IncludeSingularSolutions -> True]
 

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