62.13.1 problem Ex 1

Internal problem ID [12876]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 24. Equations solvable for \(p\). Page 49
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:31:33 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 20

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

\begin{align*} y &= -\frac {x^{2}}{2}+c_{1} \\ y &= c_{1} {\mathrm e}^{-x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 32

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

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