Internal problem ID [11210]
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]
\[ \boxed {{y^{\prime }}^{2}+y^{\prime } \left (x +y\right )+y x=0} \]
✓ 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 \left (x \right ) = -\frac {x^{2}}{2}+c_{1} y \left (x \right ) = {\mathrm e}^{-x} c_{1} \end{align*}
✓ Solution by Mathematica
Time used: 0.056 (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*}