12.6.8 problem 8

Internal problem ID [1687]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 8
Date solved : Monday, January 27, 2025 at 05:27:53 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.123 (sec). Leaf size: 51

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

\[ y = \frac {x \left (\sqrt {7}\, \tan \left (\operatorname {RootOf}\left (-3 \sqrt {7}\, \ln \left (2\right )+\sqrt {7}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} x^{2}\right )+\sqrt {7}\, \ln \left (7\right )+2 \sqrt {7}\, c_1 +2 \textit {\_Z} \right )\right )-3\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.066 (sec). Leaf size: 62

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

\[ \text {Solve}\left [\frac {\arctan \left (\frac {\frac {4 y(x)}{x}+3}{\sqrt {7}}\right )}{2 \sqrt {7}}+\frac {1}{4} \log \left (\frac {2 y(x)^2}{x^2}+\frac {3 y(x)}{x}+2\right )=-\frac {\log (x)}{2}+c_1,y(x)\right ] \]