Internal problem ID [10112]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 8. Exact
differential equations. Page 11
Problem number: Ex 5.
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 {6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.078 (sec). Leaf size: 36
dsolve((6*x-2*y(x)+1)+(2*y(x)-2*x-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \relax (x ) = 2-\frac {-\left (2 x -1\right ) c_{1}+\sqrt {-2 \left (2 x -1\right )^{2} c_{1}^{2}+1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.142 (sec). Leaf size: 63
DSolve[(6*x-2*y[x]+1)+(2*y[x]-2*x-3)*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x-\frac {1}{2} i \sqrt {8 (x-1) x-9-4 c_1}+\frac {3}{2} \\ y(x)\to x+\frac {1}{2} i \sqrt {8 (x-1) x-9-4 c_1}+\frac {3}{2} \\ \end{align*}