13.1 problem Ex 1

Internal problem ID [10186]

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.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [_quadrature]

Solve \begin {gather*} \boxed {\left (y^{\prime }\right )^{2}+\left (x +y\right ) y^{\prime }+y x=0} \end {gather*}

Solution by Maple

Time used: 0.0 (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 \relax (x ) = -\frac {x^{2}}{2}+c_{1} \\ y \relax (x ) = c_{1} {\mathrm e}^{-x} \\ \end{align*}

Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 32

DSolve[(y'[x])^2+(x+y[x])*y'[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*}