43.1.1 problem 1 (a)

Internal problem ID [8866]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 1.3 Introduction– Linear equations of First Order. Page 38
Problem number : 1 (a)
Date solved : Tuesday, September 30, 2025 at 05:58:03 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&={\mathrm e}^{3 x}+\sin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 16

ode:=diff(y(x),x) = exp(3*x)+sin(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{3 x}}{3}-\cos \left (x \right )+c_1 \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 25

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

\begin{align*} y(x)&\to \int _1^x\left (\sin (K[1])+e^{3 K[1]}\right )dK[1]+c_1 \end{align*}

✓ Sympy. Time used: 0.079 (sec). Leaf size: 14

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

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