15.18.6 problem 6

Internal problem ID [3249]
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
Date solved : Monday, January 27, 2025 at 07:28:43 AM
CAS classification : [[_2nd_order, _quadrature]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

dsolve(x*diff(y(x),x$2)=1+x^2,y(x), singsol=all)
 

\[ y \left (x \right ) = x \ln \left (x \right )+\frac {x^{3}}{6}+\left (c_{1} -1\right ) x +c_2 \]

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 25

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

\[ y(x)\to \frac {x^3}{6}+x \log (x)+(-1+c_2) x+c_1 \]