Internal problem ID [11656]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {x V^{\prime }=x^{2}+1} \] With initial conditions \begin {align*} [V \left (1\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 13
dsolve([x*diff(V(x),x)=1+x^2,V(1) = 1],V(x), singsol=all)
\[ V \left (x \right ) = \frac {x^{2}}{2}+\ln \left (x \right )+\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 18
DSolve[{x*V'[x]==1+x^2,{V[1]==1}},V[x],x,IncludeSingularSolutions -> True]
\[ V(x)\to \frac {1}{2} \left (x^2+2 \log (x)+1\right ) \]