64.4.22 problem 22(b)

Internal problem ID [13311]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 22(b)
Date solved : Tuesday, January 28, 2025 at 05:19:28 AM
CAS classification : [[_homogeneous, `class A`], _exact, _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Solution by Maple

Time used: 0.138 (sec). Leaf size: 51

dsolve((3*x-y(x))-(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {-c_{1} x -\sqrt {4 c_{1}^{2} x^{2}+1}}{c_{1}} \\ y &= \frac {-c_{1} x +\sqrt {4 c_{1}^{2} x^{2}+1}}{c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 40

DSolve[(3*x-y[x])-(x+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {K[1]+1}{(K[1]-1) (K[1]+3)}dK[1]=-\log (x)+c_1,y(x)\right ] \]