15.18.36 problem 36

Internal problem ID [3279]
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
Date solved : Monday, January 27, 2025 at 07:30:29 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} \left (1+{y^{\prime }}^{2}\right )^{2}&=y^{2} y^{\prime \prime } \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=\sqrt {2} \end{align*}

✗ Solution by Maple

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)
 

\[ \text {No solution found} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{(1+D[y[x],x]^2)^2==y[x]^2*D[y[x],{x,2}],{y[0]==3,Derivative[1][y][0] ==Sqrt[2]}},y[x],x,IncludeSingularSolutions -> True]
 

Timed out