7.7.34 problem 34

Internal problem ID [212]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Review problems at page 98
Problem number : 34
Date solved : Monday, January 27, 2025 at 02:41:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {x +3 y}{y-3 x} \end{align*}

✓ Solution by Maple

Time used: 0.024 (sec). Leaf size: 51

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

\begin{align*} y &= \frac {3 c_1 x -\sqrt {10 c_1^{2} x^{2}+1}}{c_1} \\ y &= \frac {3 c_1 x +\sqrt {10 c_1^{2} x^{2}+1}}{c_1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.438 (sec). Leaf size: 94

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

\begin{align*} y(x)\to 3 x-\sqrt {10 x^2+e^{2 c_1}} \\ y(x)\to 3 x+\sqrt {10 x^2+e^{2 c_1}} \\ y(x)\to 3 x-\sqrt {10} \sqrt {x^2} \\ y(x)\to \sqrt {10} \sqrt {x^2}+3 x \\ \end{align*}