71.5.2 problem 2

Internal problem ID [14398]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.1, page 57
Problem number : 2
Date solved : Tuesday, January 28, 2025 at 06:29:43 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 13

dsolve([diff(y(x),x)=x+1/x,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {x^{2}}{2}+\ln \left (x \right )+\frac {3}{2} \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 18

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

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