23.1.4 problem 1(d)

Internal problem ID [4094]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 2. First order equations. Exercises at page 14
Problem number : 1(d)
Date solved : Monday, January 27, 2025 at 08:08:26 AM
CAS classification : [_separable]

\begin{align*} x^{2}+x -1+\left (2 y x +y\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 55

dsolve((x^2+x-1)+(2*x*y(x)+y(x))*diff(y(x),x)=0,y(x), singsol=all)
 

\begin{align*} y \left (x \right ) &= -\frac {\sqrt {-2 x^{2}+5 \ln \left (2 x +1\right )+4 c_{1} -2 x}}{2} \\ y \left (x \right ) &= \frac {\sqrt {-2 x^{2}+5 \ln \left (2 x +1\right )+4 c_{1} -2 x}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.110 (sec). Leaf size: 73

DSolve[(x^2+x-1)+(2*x*y[x]+y[x])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{2} \sqrt {-2 x^2-2 x+5 \log (2 x+1)-\frac {1}{2}+8 c_1} \\ y(x)\to \frac {1}{2} \sqrt {-2 x^2-2 x+5 \log (2 x+1)-\frac {1}{2}+8 c_1} \\ \end{align*}