Internal problem ID [5881]
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`]]
\[ \boxed {\frac {1}{y}+\sec \left (\frac {y}{x}\right )-\frac {x y^{\prime }}{y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z} \,\operatorname {Si}\left (\textit {\_Z} \right )+\textit {\_Z} c_{1} +\textit {\_Z} x +\cos \left (\textit {\_Z} \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.145 (sec). Leaf size: 32
DSolve[(1/y[x]+Sec[y[x]/x])-x/y[x]^2*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [-\text {Si}\left (\frac {y(x)}{x}\right )-\frac {x \cos \left (\frac {y(x)}{x}\right )}{y(x)}=x+c_1,y(x)\right ] \]