Internal problem ID [2724]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 91.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G], _dAlembert]
Solve \begin {gather*} \boxed {y^{\prime } x +y-4 \sqrt {y^{\prime }}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.141 (sec). Leaf size: 63
dsolve(y(x)+x*diff(y(x),x) = 4*sqrt(diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {4 \LambertW \left (-\frac {c_{1} x}{2}\right )^{2}}{x}+8 \sqrt {\frac {\LambertW \left (-\frac {c_{1} x}{2}\right )^{2}}{x^{2}}} \\ y \relax (x ) = -\frac {4 \LambertW \left (\frac {c_{1} x}{2}\right )^{2}}{x}+8 \sqrt {\frac {\LambertW \left (\frac {c_{1} x}{2}\right )^{2}}{x^{2}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 1.297 (sec). Leaf size: 94
DSolve[y[x]+x*y'[x]==4*Sqrt[y'[x]],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {2 e^{-\frac {1}{2} \sqrt {4-x y(x)}} \left (-2 \sqrt {4-x y(x)}-4\right )}{y(x)}=c_1,y(x)\right ] \\ \text {Solve}\left [\frac {2 e^{\frac {1}{2} \sqrt {4-x y(x)}} \left (2 \sqrt {4-x y(x)}-4\right )}{y(x)}=c_1,y(x)\right ] \\ y(x)\to 0 \\ \end{align*}