44.3.28 problem 36

Internal problem ID [7009]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Review problems at page 34
Problem number : 36
Date solved : Wednesday, March 05, 2025 at 04:02:15 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 15

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

\[ y = \frac {3 x}{2}-\frac {3}{4}+c_{1} {\mathrm e}^{-2 x} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 22

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

\[ y(x)\to \frac {3 x}{2}+c_1 e^{-2 x}-\frac {3}{4} \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + \frac {3 x}{2} - \frac {3}{4} \]