29.16.3 problem 446

Internal problem ID [5044]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 16
Problem number : 446
Date solved : Monday, January 27, 2025 at 10:05:29 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.022 (sec). Leaf size: 24

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (4 \textit {\_Z} +\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 36

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

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