71.3.21 problem 16

Internal problem ID [14371]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.1, page 40
Problem number : 16
Date solved : Tuesday, January 28, 2025 at 06:27:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {2 x -y}{x +3 y} \end{align*}

✓ Solution by Maple

Time used: 0.125 (sec). Leaf size: 53

dsolve(diff(y(x),x)=(2*x-y(x))/(x+3*y(x)),y(x), singsol=all)
 

\begin{align*} y &= \frac {-c_{1} x -\sqrt {7 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ y &= \frac {-c_{1} x +\sqrt {7 c_{1}^{2} x^{2}+3}}{3 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.473 (sec). Leaf size: 114

DSolve[D[y[x],x]==(2*x-y[x])/(x+3*y[x]),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {1}{3} \left (-x-\sqrt {7 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-x+\sqrt {7 x^2+3 e^{2 c_1}}\right ) \\ y(x)\to \frac {1}{3} \left (-\sqrt {7} \sqrt {x^2}-x\right ) \\ y(x)\to \frac {1}{3} \left (\sqrt {7} \sqrt {x^2}-x\right ) \\ \end{align*}