71.6.14 problem 14

Internal problem ID [14420]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 06:30:25 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} y^{\prime }&=-\frac {y \left (2 x +y\right )}{x \left (2 y+x \right )} \end{align*}

✓ Solution by Maple

Time used: 0.102 (sec). Leaf size: 71

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

\begin{align*} y &= \frac {-c_{1}^{2} x^{2}+\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ y &= \frac {-c_{1}^{2} x^{2}-\sqrt {c_{1} x \left (c_{1}^{3} x^{3}+4\right )}}{2 c_{1}^{2} x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.120 (sec). Leaf size: 40

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

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {2 K[1]+1}{K[1] (K[1]+1)}dK[1]=-3 \log (x)+c_1,y(x)\right ] \]