85.34.1 problem 1

Internal problem ID [22709]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. B Exercises at page 67
Problem number : 1
Date solved : Thursday, October 02, 2025 at 09:11:20 PM
CAS classification : [_Bernoulli]

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

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

ode:=y(x)^2+x*y(x)*diff(y(x),x) = sin(x); 
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: 0.234 (sec). Leaf size: 50

ode=x*y[x]*D[y[x],x]+y[x]^2==Sin[x]; 
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: 0.547 (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)
 

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