28.1.67 problem 69

Internal problem ID [4373]
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 : 69
Date solved : Tuesday, March 04, 2025 at 06:33:23 PM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 36

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

\[ x +\frac {-3 y \left (x \right )^{4}-8 y \left (x \right )^{3}-6 y \left (x \right )^{2}-12 c_{1}}{12 y \left (x \right )+12} = 0 \]

✓ Mathematica. Time used: 34.061 (sec). Leaf size: 1594

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

\begin{align*} \text {Solution too large to show}\end{align*}

✓ Sympy. Time used: 47.650 (sec). Leaf size: 2717

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

\[ \text {Solution too large to show} \]