Internal problem ID [7123]
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]
\[ \boxed {\frac {y^{\prime } y}{1+\frac {\sqrt {1+{y^{\prime }}^{2}}}{2}}=-x} \] With initial conditions \begin {align*} [y \left (0\right ) = 3] \end {align*}
✓ Solution by Maple
Time used: 2.625 (sec). Leaf size: 29
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)
\begin{align*} y \left (x \right ) = -3+\sqrt {-x^{2}+36} y \left (x \right ) = 1+\sqrt {-x^{2}+4} \end{align*}
✓ Solution by Mathematica
Time used: 0.55 (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*}