Internal problem ID [12495]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {y y^{\prime \prime }-{y^{\prime }}^{2}+{y^{\prime }}^{3}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = -1, y^{\prime }\left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.063 (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)
\[ y \left (x \right ) = -1 \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{y[x]*y''[x]-(y'[x])^2+(y'[x])^3==0,{y[0]==-1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
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