48.4.7 problem Problem 3.8

Internal problem ID [7549]
Book : THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T. CHAU, CRC Press. Boca Raton, FL. 2018
Section : Chapter 3. Ordinary Differential Equations. Section 3.6 Summary and Problems. Page 218
Problem number : Problem 3.8
Date solved : Monday, January 27, 2025 at 03:05:15 PM
CAS classification : [[_homogeneous, `class D`]]

\begin{align*} \frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 20

dsolve((1/y(x)+sec(y(x)/x))-x/y(x)^2*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (\textit {\_Z} \,\operatorname {Si}\left (\textit {\_Z} \right )+\textit {\_Z} c_{1} +x \textit {\_Z} +\cos \left (\textit {\_Z} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.172 (sec). Leaf size: 32

DSolve[(1/y[x]+Sec[y[x]/x])-x/y[x]^2*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [-\text {Si}\left (\frac {y(x)}{x}\right )-\frac {x \cos \left (\frac {y(x)}{x}\right )}{y(x)}=x+c_1,y(x)\right ] \]