89.6.41 problem 42

Internal problem ID [24424]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Miscellaneous Exercises at page 45
Problem number : 42
Date solved : Thursday, October 02, 2025 at 10:27:44 PM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 13

ode:=diff(y(x),x) = 3*x+y(x); 
ic:=[y(-1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -3 x -3+{\mathrm e}^{x +1} \]

✓ Mathematica. Time used: 0.018 (sec). Leaf size: 16

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

\begin{align*} y(x)&\to e^{x+1}-3 (x+1) \end{align*}

✓ Sympy. Time used: 0.066 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x - y(x) + Derivative(y(x), x),0) 
ics = {y(-1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - 3 x + e e^{x} - 3 \]