Internal problem ID [10889]
Book: APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin.
CRC Press 2015
Section: Chapter 4, Second and Higher Order Linear Differential Equations. Problems page
221
Problem number: Problem 2(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-x^{2}-y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)=x^2+y(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}+c_{1} {\mathrm e}^{-x}-x^{2}-2 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 26
DSolve[y''[x]==x^2+y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x^2+c_1 e^x+c_2 e^{-x}-2 \\ \end{align*}