4.22 problem Problem 3.35

Internal problem ID [5143]

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 3.35.
ODE order: 1.
ODE degree: 1.

CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]

Solve \begin {gather*} \boxed {x +y^{\prime } y+y-x y^{\prime }=0} \end {gather*}

Solution by Maple

Time used: 0.031 (sec). Leaf size: 24

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

\[ y \relax (x ) = \tan \left (\RootOf \left (-2 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x \]

Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 36

DSolve[x+y[x]*y'[x]+y[x]-x*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+1\right )-\text {ArcTan}\left (\frac {y(x)}{x}\right )=-\log (x)+c_1,y(x)\right ] \]