64.6.5 problem 5

Internal problem ID [13355]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Miscellaneous Review. Exercises page 60
Problem number : 5
Date solved : Tuesday, January 28, 2025 at 05:31:37 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 x -5 y+\left (x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 47

dsolve((3*x-5*y(x))+(x+y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y &= \frac {6 c_{1} x +1-\sqrt {8 c_{1} x +1}}{2 c_{1}} \\ y &= \frac {6 c_{1} x +1+\sqrt {8 c_{1} x +1}}{2 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.037 (sec). Leaf size: 40

DSolve[(3*x-5*y[x])+(x+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

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