Internal problem ID [1987]
Book: Mathematical methods for physics and engineering, Riley, Hobson, Bence, second edition,
2002
Section: Chapter 14, First order ordinary differential equations. 14.4 Exercises, page 490
Problem number: Problem 14.11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (y-x \right ) y^{\prime }+2 x +3 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.018 (sec). Leaf size: 28
dsolve((y(x)-x)*diff(y(x),x)+2*x+3*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \tan \left (\RootOf \left (-4 \textit {\_Z} +\ln \left (\frac {1}{\cos \left (\textit {\_Z} \right )^{2}}\right )+2 \ln \relax (x )+2 c_{1}\right )\right ) x -x \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 45
DSolve[(y[x]-x)*y'[x]+2*x+3*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [\frac {1}{2} \log \left (\frac {y(x)^2}{x^2}+\frac {2 y(x)}{x}+2\right )-2 \text {ArcTan}\left (\frac {y(x)}{x}+1\right )=-\log (x)+c_1,y(x)\right ] \]