Internal problem ID [11126]
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`]]
\[ \boxed {-2 y+\left (2 y-2 x -3\right ) y^{\prime }=-6 x -1} \]
✓ Solution by Maple
Time used: 0.469 (sec). Leaf size: 33
dsolve((6*x-2*y(x)+1)+(2*y(x)-2*x-3)*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {-\sqrt {1-8 \left (x -\frac {1}{2}\right )^{2} c_{1}^{2}}+\left (2 x +3\right ) c_{1}}{2 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.208 (sec). Leaf size: 67
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 -\frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ y(x)\to \frac {1}{2} i \sqrt {8 x^2-8 x-9-4 c_1}+x+\frac {3}{2} \\ \end{align*}