89.8.7 problem 8

Internal problem ID [24467]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 4. Additional topics on equations of first order and first degree. Exercises at page 66
Problem number : 8
Date solved : Thursday, October 02, 2025 at 10:39:55 PM
CAS classification : [[_linear, `class A`]]

\begin{align*} x -y+2+3 y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=x-y(x)+2+3*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x +5+{\mathrm e}^{\frac {x}{3}} c_1 \]

✓ Mathematica. Time used: 0.051 (sec). Leaf size: 18

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

\begin{align*} y(x)&\to x+c_1 e^{x/3}+5 \end{align*}

✓ Sympy. Time used: 0.078 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} e^{\frac {x}{3}} + x + 5 \]