Internal problem ID [3809]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1116.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class C], _dAlembert]
Solve \begin {gather*} \boxed {\left (x -y\right ) \sqrt {y^{\prime }}-a \left (y^{\prime }+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.195 (sec). Leaf size: 44
dsolve((x-y(x))*sqrt(diff(y(x),x)) = a*(1+diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \relax (x ) = x -2 a \\ y \relax (x ) = x +\frac {-\frac {a^{3}}{\left (c_{1}-x \right )^{2}}-a}{\sqrt {\frac {a^{2}}{\left (c_{1}-x \right )^{2}}}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 65.233 (sec). Leaf size: 10217
DSolve[(x-y[x]) Sqrt[y'[x]]== a (1+y'[x]),y[x],x,IncludeSingularSolutions -> True]
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