67.7.35 problem 35

Internal problem ID [16480]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 35
Date solved : Thursday, October 02, 2025 at 01:35:04 PM
CAS classification : [_linear]

\begin{align*} 2 y-6 x +\left (1+x \right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 22

ode:=2*y(x)-6*x+(1+x)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {2 x^{3}+3 x^{2}+c_1}{\left (x +1\right )^{2}} \]

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 24

ode=(2*y[x]-6*x)+(x+1)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {2 x^3+3 x^2+c_1}{(x+1)^2} \end{align*}

✓ Sympy. Time used: 0.155 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-6*x + (x + 1)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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