10.5.2 problem 2

Internal problem ID [1194]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.6. Page 100
Problem number : 2
Date solved : Monday, January 27, 2025 at 04:43:42 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 2 x +4 y+\left (2 x -2 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.153 (sec). Leaf size: 55

dsolve(2*x+4*y(x)+(2*x-2*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\[ -\frac {\ln \left (\frac {-x^{2}-3 x y+y^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {13}\, \operatorname {arctanh}\left (\frac {\left (2 y-3 x \right ) \sqrt {13}}{13 x}\right )}{13}-\ln \left (x \right )-c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 63

DSolve[2*x+4*y[x]+(2*x-2*y[x])*D[y[x],x]== 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\frac {1}{26} \left (\left (13+\sqrt {13}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {13}+3\right )-\left (\sqrt {13}-13\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {13}-3\right )\right )=-\log (x)+c_1,y(x)\right ] \]