Internal problem ID [2278]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _quadrature]]
\[ \boxed {x y^{\prime \prime }=x^{2}+1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(x*diff(y(x),x$2)=1+x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{6}+x \ln \left (x \right )-x +c_{1} x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.004 (sec). Leaf size: 25
DSolve[x*y''[x]==1+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{6}+x \log (x)+(-1+c_2) x+c_1 \]