2.8.1 problem 21

Internal problem ID [838]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.2, second order linear equations. Page 311
Problem number : 21
Date solved : Tuesday, September 30, 2025 at 04:15:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }+y&=3 x \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \\ y^{\prime }\left (0\right )&=-2 \\ \end{align*}

✓ Maple. Time used: 0.045 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)+y(x) = 3*x; 
ic:=[y(0) = 2, D(y)(0) = -2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -5 \sin \left (x \right )+2 \cos \left (x \right )+3 x \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 17

ode=D[y[x],{x,2}]+y[x]==3*x; 
ic={y[0]==2,Derivative[1][y][0] ==-2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 3 x-5 \sin (x)+2 \cos (x) \end{align*}

✓ Sympy. Time used: 0.036 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x + y(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 2, Subs(Derivative(y(x), x), x, 0): -2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 3 x - 5 \sin {\left (x \right )} + 2 \cos {\left (x \right )} \]