81.3.9 problem 9

Internal problem ID [18627]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter III. Ordinary differential equations of the first order and first degree. Exercises at page 33
Problem number : 9
Date solved : Tuesday, January 28, 2025 at 12:04:39 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 15

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

\[ y \left (x \right ) = \frac {1}{{\mathrm e}^{-\cos \left (x \right )} c_{1} +1} \]

✓ Solution by Mathematica

Time used: 0.344 (sec). Leaf size: 31

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

\begin{align*} y(x)\to \frac {e^{\cos (x)}}{e^{\cos (x)}+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}