14.33 problem 359

Internal problem ID [15217]

Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number: 359.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\[ \boxed {y^{3} y^{\prime \prime }=-1} \] With initial conditions \begin {align*} [y \left (1\right ) = 1, y^{\prime }\left (1\right ) = 0] \end {align*}

✗ Solution by Maple

dsolve([y(x)^3*diff(y(x),x$2)=-1,y(1) = 1, D(y)(1) = 0],y(x), singsol=all)
 

\[ \text {No solution found} \]

✓ Solution by Mathematica

Time used: 0.051 (sec). Leaf size: 15

DSolve[{y[x]^3*y''[x]==-1,{y[1]==1,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
                                                                                    
                                                                                    
 

\[ y(x)\to \sqrt {-((x-2) x)} \]