Internal problem ID [4158]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 8. Special second order equations. Lesson 35. Independent variable x
absent
Problem number: Exercise 35.16, page 504.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
Solve \begin {gather*} \boxed {\left (1+y\right ) y^{\prime \prime }-3 \left (y^{\prime }\right )^{2}=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (1) = 0, y^{\prime }\relax (1) = -{\frac {1}{2}}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.953 (sec). Leaf size: 15
dsolve([(y(x)+1)*diff(y(x),x$2)=3*(diff(y(x),x))^2,y(1) = 0, D(y)(1) = -1/2],y(x), singsol=all)
\[ y \relax (x ) = \frac {-x +\sqrt {x}}{x} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(y[x]+1)*y''[x]==3*(y'[x])^3,{y[1]==0,y'[0]==-1/2}},y[x],x,IncludeSingularSolutions -> True]
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