Internal problem ID [4021]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 12, Miscellaneous
Methods
Problem number: Exercise 12.8, page 103.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _exact, _rational, [_Abel, 2nd type, class A]]
Solve \begin {gather*} \boxed {\left (3 x +2 y+1\right ) y^{\prime }+4 x +3 y+2=0} \end {gather*}
✓ Solution by Maple
Time used: 0.717 (sec). Leaf size: 33
dsolve((3*x+2*y(x)+1)*diff(y(x),x)+(4*x+3*y(x)+2)=0,y(x), singsol=all)
\[ y \relax (x ) = -2-\frac {\frac {3 c_{1} \left (x -1\right )}{2}+\frac {\sqrt {\left (x -1\right )^{2} c_{1}^{2}+4}}{2}}{c_{1}} \]
✓ Solution by Mathematica
Time used: 0.097 (sec). Leaf size: 57
DSolve[(3*x+2*y[x]+1)*y'[x]+(4*x+3*y[x]+2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (-3 x-\sqrt {(x-1)^2+4 c_1}-1\right ) \\ y(x)\to \frac {1}{2} \left (-3 x+\sqrt {(x-1)^2+4 c_1}-1\right ) \\ \end{align*}