67.2.16 problem Problem 2(a)

Internal problem ID [13973]
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)
Date solved : Tuesday, January 28, 2025 at 06:10:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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

\[ y = c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} c_{1} -x^{2}-2 \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 26

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

\[ y(x)\to -x^2+c_1 e^x+c_2 e^{-x}-2 \]