22.1.40 problem 41

Internal problem ID [4346]
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 : 41
Date solved : Tuesday, September 30, 2025 at 07:20:52 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} x^{2}+y+y^{2}-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 10

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

\[ y = \tan \left (x +c_1 \right ) x \]

✓ Mathematica. Time used: 0.132 (sec). Leaf size: 12

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

\begin{align*} y(x)&\to x \tan (x+c_1) \end{align*}

✓ Sympy. Time used: 0.196 (sec). Leaf size: 24

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

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