80.3.5 problem 5

Internal problem ID [18549]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter IV. Methods of solution: First order equations. section 29. Problems at page 81
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 11:57:50 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} x +y^{\prime } y&=m y \end{align*}

✓ Solution by Maple

Time used: 0.085 (sec). Leaf size: 57

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

\[ y \left (x \right ) = \operatorname {RootOf}\left (\textit {\_Z}^{2}-{\mathrm e}^{\operatorname {RootOf}\left (\left (4 \,{\mathrm e}^{\textit {\_Z}} {\cosh \left (\frac {\sqrt {m^{2}-4}\, \left (2 c_{1} +\textit {\_Z} +2 \ln \left (x \right )\right )}{2 m}\right )}^{2}+m^{2}-4\right ) x^{2}\right )}+1-\textit {\_Z} m \right ) x \]

✓ Solution by Mathematica

Time used: 0.092 (sec). Leaf size: 72

DSolve[x+y[x]*D[y[x],x]==m*y[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {m \arctan \left (\frac {\frac {2 y(x)}{x}-m}{\sqrt {4-m^2}}\right )}{\sqrt {4-m^2}}+\frac {1}{2} \log \left (-\frac {m y(x)}{x}+\frac {y(x)^2}{x^2}+1\right )=-\log (x)+c_1,y(x)\right ] \]