40.1.8 problem 20

Internal problem ID [6576]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 2. Solutions of differential equations. Supplemetary problems. Page 11
Problem number : 20
Date solved : Sunday, March 30, 2025 at 11:10:14 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-y&=4-x \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 17

ode:=diff(diff(y(x),x),x)-y(x) = -x+4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} c_2 +{\mathrm e}^{x} c_1 -4+x \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 22

ode=D[y[x],{x,2}]-y[x]==4-x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x+c_1 e^x+c_2 e^{-x}-4 \]

✓ Sympy. Time used: 0.074 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x - y(x) + Derivative(y(x), (x, 2)) - 4,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- x} + C_{2} e^{x} + x - 4 \]