65.1.9 problem 5.4 (iv)

Internal problem ID [13712]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 5, Trivial differential equations. Exercises page 33
Problem number : 5.4 (iv)
Date solved : Tuesday, January 28, 2025 at 05:55:48 AM
CAS classification : [_quadrature]

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

With initial conditions

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

✓ Solution by Maple

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

dsolve([x*diff(V(x),x)=1+x^2,V(1) = 1],V(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 18

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

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