Internal problem ID [2308]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 35, page 157
Problem number: 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]
\[ \boxed {\left (1+{y^{\prime }}^{2}\right )^{2}-y^{2} y^{\prime \prime }=0} \] With initial conditions \begin {align*} \left [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = \sqrt {2}\right ] \end {align*}
✓ Solution by Maple
Time used: 75.984 (sec). Leaf size: 221
dsolve([(1+diff(y(x),x)^2)^2=y(x)^2*diff(y(x),x$2),y(0) = 3, D(y)(0) = 2^(1/2)],y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \operatorname {RootOf}\left (\sqrt {2}\, \left (\int _{\textit {\_Z}}^{3}\frac {\operatorname {RootOf}\left (\left (-\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} -1}{\sqrt {-\left (\operatorname {RootOf}\left (\left (-\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} -1\right ) \left (2 \operatorname {RootOf}\left (\left (-\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} +\textit {\_a} -2\right )}}d \textit {\_a} \right )+x \right ) \\ y \left (x \right ) &= \operatorname {RootOf}\left (\sqrt {2}\, \left (\int _{3}^{\textit {\_Z}}\frac {\operatorname {RootOf}\left (\left (\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} -1}{\sqrt {-\left (\operatorname {RootOf}\left (\left (\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} -1\right ) \left (2 \operatorname {RootOf}\left (\left (\sqrt {-\left (3 \textit {\_Z} -1\right ) \left (6 \textit {\_Z} +1\right )}+6 \textit {\_Z} -2\right ) \sqrt {2}\right ) \textit {\_a} +\textit {\_a} -2\right )}}d \textit {\_a} \right )+x \right ) \\ \end{align*}
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(1+y'[x]^2)^2==y[x]^2*y''[x],{y[0]==3,y'[0]==Sqrt[2]}},y[x],x,IncludeSingularSolutions -> True]
Timed out