83.2.3 problem 3

Internal problem ID [19049]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter II. Equations of first order and first degree. Exercise II (A) at page 8
Problem number : 3
Date solved : Tuesday, January 28, 2025 at 12:48:07 PM
CAS classification : [_Bernoulli]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 12

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

\[ y \left (x \right ) = \frac {\sin \left (x \right )}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 19

DSolve[Sin[x]*D[y[x],x]-y[x]*Cos[x]+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {\sin (x)}{x+c_1} \\ y(x)\to 0 \\ \end{align*}