4.7 problem Problem 3.8

Internal problem ID [5128]

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.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class D]]

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

Solution by Maple

Time used: 0.062 (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)
 

\[ y \relax (x ) = \RootOf \left (\textit {\_Z} \sinIntegral \left (\textit {\_Z} \right )+c_{1} \textit {\_Z} +\textit {\_Z} x +\cos \left (\textit {\_Z} \right )\right ) x \]

Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 32

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

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