10.6.29 problem 29

Internal problem ID [1246]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 29
Date solved : Monday, January 27, 2025 at 04:47:37 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 24

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

\[ y = \tan \left (\operatorname {RootOf}\left (-2 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_1 \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 36

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

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