64.4.14 problem 14

Internal problem ID [13303]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.2 (Separable equations). Exercises page 47
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 05:17:06 AM
CAS classification : [[_homogeneous, `class C`], _dAlembert]

\begin{align*} \sqrt {x +y}+\sqrt {x -y}+\left (\sqrt {x -y}-\sqrt {x +y}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 8.701 (sec). Leaf size: 36

dsolve((sqrt(x+y(x))+sqrt(x-y(x)))+(sqrt(x-y(x))-sqrt(x+y(x)))*diff(y(x),x)=0,y(x), singsol=all)
 

\[ \ln \left (x \right )+\ln \left (\frac {y}{x}\right )-\operatorname {arctanh}\left (\frac {1}{\sqrt {-\frac {y^{2}-x^{2}}{x^{2}}}}\right )-c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 3.609 (sec). Leaf size: 52

DSolve[(Sqrt[x+y[x]]+Sqrt[x-y[x]])+(Sqrt[x-y[x]]-Sqrt[x+y[x]])*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to \sqrt {-e^{c_1} \left (-2 x+e^{c_1}\right )} \\ y(x)\to 0 \\ \end{align*}