27.22 problem 788

Internal problem ID [3520]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 27
Problem number: 788.
ODE order: 1.
ODE degree: 2.

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

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

Solution by Maple

Time used: 0.172 (sec). Leaf size: 32

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

\begin{align*} y \relax (x ) = -\frac {1}{4} x^{2}-\frac {1}{2} a x -\frac {1}{4} a^{2} \\ y \relax (x ) = c_{1} a +c_{1} x +c_{1}^{2} \\ \end{align*}

Solution by Mathematica

Time used: 0.006 (sec). Leaf size: 26

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

\begin{align*} y(x)\to c_1 (a+x+c_1) \\ y(x)\to -\frac {1}{4} (a+x)^2 \\ \end{align*}