87.1.15 problem 16

Internal problem ID [23227]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 1. Elementary methods. First order differential equations. Exercise at page 9
Problem number : 16
Date solved : Thursday, October 02, 2025 at 09:24:36 PM
CAS classification : [[_2nd_order, _missing_x]]

\begin{align*} y+2 y^{\prime }+y^{\prime \prime }&=1 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 1; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 1+\left (c_1 x +c_2 \right ) {\mathrm e}^{-x} \]

✓ Mathematica. Time used: 0.011 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.111 (sec). Leaf size: 12

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

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