20.4.20 problem Problem 29(a)

Internal problem ID [3655]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.8, Change of Variables. page 79
Problem number : Problem 29(a)
Date solved : Monday, January 27, 2025 at 07:52:11 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +a y}{a x -y} \end{align*}

✓ Solution by Maple

Time used: 0.513 (sec). Leaf size: 25

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} a +\ln \left (\sec \left (\textit {\_Z} \right )^{2} x^{2}\right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.040 (sec). Leaf size: 34

DSolve[D[y[x],x]==(x+a*y[x])/(a*x-y[x]),y[x],x,IncludeSingularSolutions -> True]
 

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