23.3.28 problem 28

Internal problem ID [5742]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 3. THE DIFFERENTIAL EQUATION IS LINEAR AND OF SECOND ORDER, page 311
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 02:02:23 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 32

ode:=diff(diff(y(x),x),x) = a*x+b*y(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{\sqrt {b}\, x} c_2 b +{\mathrm e}^{-\sqrt {b}\, x} c_1 b -a x}{b} \]

✓ Mathematica. Time used: 0.01 (sec). Leaf size: 38

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

\begin{align*} y(x)&\to -\frac {a x}{b}+c_1 e^{\sqrt {b} x}+c_2 e^{-\sqrt {b} x} \end{align*}

✓ Sympy. Time used: 0.052 (sec). Leaf size: 27

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

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