61.2.16 problem Problem 2(a)

Internal problem ID [15254]
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 : Thursday, October 02, 2025 at 10:08:57 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

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

ode:=diff(diff(y(x),x),x) = y(x)+x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{x} c_1 -x^{2}-2 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 26

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

\begin{align*} y(x)&\to -x^2+c_1 e^x+c_2 e^{-x}-2 \end{align*}

✓ Sympy. Time used: 0.038 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 - y(x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} - x^{2} - 2 \]