88.15.3 problem 3

Internal problem ID [24099]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 4. Linear equations. Exercises at page 97
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:59:13 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 4 y+y^{\prime \prime }&=1-x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=0 \\ y^{\prime }\left (0\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.012 (sec). Leaf size: 21

ode:=diff(diff(y(x),x),x)+4*y(x) = 1-x; 
ic:=[y(0) = 0, D(y)(0) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 x \right )}{8}-\frac {\cos \left (2 x \right )}{4}-\frac {x}{4}+\frac {1}{4} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 24

ode=D[y[x],{x,2}]+4*y[x]==1-x; 
ic={y[0]==0,Derivative[1][y][0] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{8} (-2 x+\sin (2 x)-2 \cos (2 x)+2) \end{align*}

✓ Sympy. Time used: 0.051 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + 4*y(x) + Derivative(y(x), (x, 2)) - 1,0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {x}{4} + \frac {\sin {\left (2 x \right )}}{8} - \frac {\cos {\left (2 x \right )}}{4} + \frac {1}{4} \]