69.1.78 problem 123

Internal problem ID [14231]
Book : DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR PUBLISHERS, Moscow 1969.
Section : Chapter 8. Differential equations. Exercises page 595
Problem number : 123
Date solved : Tuesday, January 28, 2025 at 06:22:46 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.105 (sec). Leaf size: 5

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

\[ y = -1 \]

✗ Solution by Mathematica

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

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

{}