22.1.66 problem 68

Internal problem ID [4372]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page 78
Problem number : 68
Date solved : Tuesday, September 30, 2025 at 07:23:39 AM
CAS classification : [_linear]

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

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

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

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

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 20

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

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

✓ Sympy. Time used: 0.150 (sec). Leaf size: 17

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

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