73.7.40 problem 40

Internal problem ID [15198]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 40
Date solved : Tuesday, January 28, 2025 at 07:41:51 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 13

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

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

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 29

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

\begin{align*} y(x)\to -\frac {1}{\int _1^x(\cos (K[1])-1)dK[1]+c_1} \\ y(x)\to 0 \\ \end{align*}