67.2.1 problem 3.4 a

Internal problem ID [16311]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 3. Some basics about First order equations. Additional exercises. page 63
Problem number : 3.4 a
Date solved : Thursday, October 02, 2025 at 10:45:36 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+3 y x&=6 x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

ode:=diff(y(x),x)+3*x*y(x) = 6*x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = 2+{\mathrm e}^{-\frac {3 x^{2}}{2}} c_1 \]

✓ Mathematica. Time used: 0.048 (sec). Leaf size: 24

ode=D[y[x],x]+3*x*y[x]==6*x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2+c_1 e^{-\frac {3 x^2}{2}}\\ y(x)&\to 2 \end{align*}

✓ Sympy. Time used: 0.182 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*y(x) - 6*x + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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