10.6.30 problem 30

Internal problem ID [1247]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 30
Date solved : Monday, January 27, 2025 at 04:47:41 AM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class B`]]

\begin{align*} 2 y x +3 y^{2}-\left (x^{2}+2 y x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 33

dsolve(2*x*y(x)+3*y(x)^2-(x^2+2*x*y(x))*diff(y(x),x) = 0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (1+\sqrt {4 c_1 x +1}\right ) x}{2} \\ y &= \frac {\left (-1+\sqrt {4 c_1 x +1}\right ) x}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.390 (sec). Leaf size: 61

DSolve[2*x*y[x]+3*y[x]^2-(x^2+2*x*y[x])*D[y[x],x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} x \left (1+\sqrt {1+4 e^{c_1} x}\right ) \\ y(x)\to \frac {1}{2} x \left (-1+\sqrt {1+4 e^{c_1} x}\right ) \\ y(x)\to 0 \\ y(x)\to -x \\ \end{align*}