7.5.32 problem 32

Internal problem ID [136]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 32
Date solved : Friday, February 07, 2025 at 07:56:35 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.040 (sec). Leaf size: 51

dsolve((4*x-y(x))+(6*y(x)-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: 0.486 (sec). Leaf size: 106

DSolve[(4*x-y[x])+(6*y[x]-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*}