Internal problem ID [4317]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 37
Problem number: 1116.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\left (x -y\right ) \sqrt {y^{\prime }}-a \left (1+y^{\prime }\right )=0} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 48
dsolve((x-y(x))*sqrt(diff(y(x),x)) = a*(1+diff(y(x),x)),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= x -2 a \\ y \left (x \right ) &= x -\frac {a \left (a^{2}+\left (x -c_{1} \right )^{2}\right )}{\sqrt {\frac {a^{2}}{\left (c_{1} -x \right )^{2}}}\, \left (x -c_{1} \right )^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 69.72 (sec). Leaf size: 9683
DSolve[(x-y[x])*Sqrt[y'[x]]== a*(1+y'[x]),y[x],x,IncludeSingularSolutions -> True]
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