Internal problem ID [6370]
Book: Own collection of miscellaneous problems
Section: section 1.0
Problem number: 78.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class A], _dAlembert]
Solve \begin {gather*} \boxed {\frac {y^{\prime } y}{1+\frac {\sqrt {1+\left (y^{\prime }\right )^{2}}}{2}}+x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 3] \end {align*}
✗ Solution by Maple
dsolve([diff(y(x),x)*y(x)/(1+1/2*sqrt(1+diff(y(x),x)^2))=-x,y(0) = 3],y(x), singsol=all)
\[ \text {No solution found} \]
✓ Solution by Mathematica
Time used: 0.771 (sec). Leaf size: 35
DSolve[{y'[x]*y[x]/(1+1/2*Sqrt[1+(y'[x])^2])==-x,y[0]==3},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {4-x^2}+1 \\ y(x)\to \sqrt {36-x^2}-3 \\ \end{align*}