28.1.73 problem 76

Internal problem ID [4379]
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 : 76
Date solved : Sunday, March 30, 2025 at 03:11:09 AM
CAS classification : [_Bernoulli]

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

✓ Maple. Time used: 0.013 (sec). Leaf size: 42

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

\begin{align*} y &= \frac {\sqrt {2 \sin \left (x \right )-2 x \cos \left (x \right )+c_1}}{x} \\ y &= -\frac {\sqrt {2 \sin \left (x \right )-2 x \cos \left (x \right )+c_1}}{x} \\ \end{align*}

✓ Mathematica. Time used: 0.328 (sec). Leaf size: 50

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

\begin{align*} y(x)\to -\frac {\sqrt {2 \sin (x)-2 x \cos (x)+c_1}}{x} \\ y(x)\to \frac {\sqrt {2 \sin (x)-2 x \cos (x)+c_1}}{x} \\ \end{align*}

✓ Sympy. Time used: 0.838 (sec). Leaf size: 42

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

\[ \left [ y{\left (x \right )} = - \frac {\sqrt {C_{1} - 2 x \cos {\left (x \right )} + 2 \sin {\left (x \right )}}}{x}, \ y{\left (x \right )} = \frac {\sqrt {C_{1} - 2 x \cos {\left (x \right )} + 2 \sin {\left (x \right )}}}{x}\right ] \]