15.8.3 problem 3

Internal problem ID [3006]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:07:33 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +y-\left (x -2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 24

dsolve((2*x+y(x))-(x-2*y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 32

DSolve[(2*x+y[x])-(x-2*y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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