Internal problem ID [11207]
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 25. Equations solvable for \(y\). Page 52
Problem number: Ex 2.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {4 x {y^{\prime }}^{2}+2 y^{\prime } x -y=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 35
dsolve(4*x*diff(y(x),x)^2+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= -\frac {x}{4} \\ y \left (x \right ) &= 4 c_{1} +2 \sqrt {c_{1} x} \\ y \left (x \right ) &= 4 c_{1} -2 \sqrt {c_{1} x} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.196 (sec). Leaf size: 72
DSolve[4*x*(y'[x])^2+2*x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{2 c_1} \left (-2 \sqrt {x}+e^{2 c_1}\right ) \\ y(x)\to \frac {1}{4} e^{-4 c_1} \left (1+2 e^{2 c_1} \sqrt {x}\right ) \\ y(x)\to 0 \\ y(x)\to -\frac {x}{4} \\ \end{align*}