29.37.3 problem 1116

Internal problem ID [5661]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 37
Problem number : 1116
Date solved : Monday, January 27, 2025 at 01:02:11 PM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \left (x -y\right ) \sqrt {y^{\prime }}&=a \left (1+y^{\prime }\right ) \end{align*}

✓ Solution by Maple

Time used: 0.135 (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 {\left (a^{2}+\left (-c_{1} +x \right )^{2}\right ) a}{\sqrt {\frac {a^{2}}{\left (-x +c_{1} \right )^{2}}}\, \left (-c_{1} +x \right )^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 27.693 (sec). Leaf size: 12141

DSolve[(x-y[x])*Sqrt[D[y[x],x]]== a*(1+D[y[x],x]),y[x],x,IncludeSingularSolutions -> True]
 

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