Internal problem ID [11637]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class C`], _dAlembert]
\[ \boxed {\sqrt {x +y}+\sqrt {-y+x}+\left (\sqrt {-y+x}-\sqrt {x +y}\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 3.781 (sec). Leaf size: 32
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)
\[ \ln \left (x \right )+\ln \left (\frac {y \left (x \right )}{x}\right )-\operatorname {arctanh}\left (\frac {1}{\sqrt {-\frac {y \left (x \right )^{2}}{x^{2}}+1}}\right )-c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 2.828 (sec). Leaf size: 84
DSolve[(Sqrt[x+y[x]]+Sqrt[x-y[x]])+(Sqrt[x-y[x]]-Sqrt[x+y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {-8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to \frac {1}{4} \left (\cosh \left (\frac {c_1}{2}\right )+\sinh \left (\frac {c_1}{2}\right )\right ) \sqrt {-8 i x+\cosh (c_1)+\sinh (c_1)} y(x)\to 0 \end{align*}