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 : Monday, January 27, 2025 at 09:09:39 AM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.048 (sec). Leaf size: 42

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

\begin{align*} y \left (x \right ) &= \frac {\sqrt {2 \sin \left (x \right )-2 \cos \left (x \right ) x +c_{1}}}{x} \\ y \left (x \right ) &= -\frac {\sqrt {2 \sin \left (x \right )-2 \cos \left (x \right ) x +c_{1}}}{x} \\ \end{align*}

✓ Solution by Mathematica

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

DSolve[x*y[x]*D[y[x],x]+y[x]^2-Sin[x]==0,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*}