Internal problem ID [544]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.6. Page 100
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]
\[ \boxed {2 x +4 y+\left (2 x -2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 56
dsolve(2*x+4*y(x)+(2*x-2*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
\[ -\frac {\ln \left (-\frac {x^{2}+3 x y \left (x \right )-y \left (x \right )^{2}}{x^{2}}\right )}{2}-\frac {\sqrt {13}\, \operatorname {arctanh}\left (\frac {\left (-2 y \left (x \right )+3 x \right ) \sqrt {13}}{13 x}\right )}{13}-\ln \left (x \right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.067 (sec). Leaf size: 63
DSolve[2*x+4*y[x]+(2*x-2*y[x])*y'[x]== 0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{26} \left (\left (13+\sqrt {13}\right ) \log \left (-\frac {2 y(x)}{x}+\sqrt {13}+3\right )-\left (\sqrt {13}-13\right ) \log \left (\frac {2 y(x)}{x}+\sqrt {13}-3\right )\right )=-\log (x)+c_1,y(x)\right ] \]