8.5.32 problem 32

Internal problem ID [760]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 32
Date solved : Wednesday, February 05, 2025 at 03:58:18 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x -y+\left (-x +6 y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 51

dsolve(4*x-y(x)+(-x+6*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\begin{align*} y &= \frac {c_1 x -\sqrt {-23 c_1^{2} x^{2}+12}}{6 c_1} \\ y &= \frac {c_1 x +\sqrt {-23 c_1^{2} x^{2}+12}}{6 c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.392 (sec). Leaf size: 106

DSolve[4*x-y[x]+(-x+6*y[x])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{6} \left (x-\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x+\sqrt {-23 x^2+12 e^{c_1}}\right ) \\ y(x)\to \frac {1}{6} \left (x-\sqrt {23} \sqrt {-x^2}\right ) \\ y(x)\to \frac {1}{6} \left (\sqrt {23} \sqrt {-x^2}+x\right ) \\ \end{align*}