5.2 problem 2

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`]]

\[ \boxed {4 y+\left (2 x -2 y\right ) y^{\prime }=-2 x} \]

Solution by Maple

Time used: 0.14 (sec). Leaf size: 55

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

\[ -\frac {\ln \left (\frac {-x^{2}-3 x y \left (x \right )+y \left (x \right )^{2}}{x^{2}}\right )}{2}+\frac {\sqrt {13}\, \operatorname {arctanh}\left (\frac {\left (2 y \left (x \right )-3 x \right ) \sqrt {13}}{13 x}\right )}{13}-\ln \left (x \right )-c_{1} = 0 \]

Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 63

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

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