30.2 problem 860

Internal problem ID [3590]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 30
Problem number: 860.
ODE order: 1.
ODE degree: 2.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational, _Clairaut]

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

Solution by Maple

Time used: 0.234 (sec). Leaf size: 27

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

\begin{align*} y \relax (x ) = c_{1} x +\frac {c_{1} a +b}{c_{1}} \\ y \relax (x ) = c_{1} \sqrt {x}+a \\ \end{align*}

Solution by Mathematica

Time used: 0.014 (sec). Leaf size: 58

DSolve[x (y'[x])^2+(a-y[x])y'[x]+b==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to a+\frac {b}{c_1}+c_1 x \\ y(x)\to \text {Indeterminate} \\ y(x)\to a-2 \sqrt {b} \sqrt {x} \\ y(x)\to a+2 \sqrt {b} \sqrt {x} \\ \end{align*}