75.14.33 problem 359

Internal problem ID [16947]
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 ODEs). Section 14. Differential equations admitting of depression of their order. Exercises page 107
Problem number : 359
Date solved : Tuesday, January 28, 2025 at 09:43:03 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} y^{3} y^{\prime \prime }&=-1 \end{align*}

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: 0.055 (sec). Leaf size: 15

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

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