62.1.5 problem Ex 5

Internal problem ID [12802]
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
Date solved : Tuesday, January 28, 2025 at 04:21:29 AM
CAS classification : [[_homogeneous, `class C`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 6 x -2 y+1+\left (2 y-2 x -3\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 1.544 (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)
 

\[ y = \frac {-\sqrt {1-8 \left (-\frac {1}{2}+x \right )^{2} c_{1}^{2}}+\left (2 x +3\right ) c_{1}}{2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.149 (sec). Leaf size: 67

DSolve[(6*x-2*y[x]+1)+(2*y[x]-2*x-3)*D[y[x],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*}