Internal problem ID [15454]
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 17. Boundary value problems. Exercises page
163
Problem number: 710.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{2}=-1} \] With initial conditions \begin {align*} [y \left (0\right ) = 1, y \left (1\right ) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.781 (sec). Leaf size: 16
dsolve([y(x)*diff(y(x),x$2)+diff(y(x),x)^2+1=0,y(0) = 1, y(1) = 2],y(x), singsol=all)
\[ y \left (x \right ) = \sqrt {-x^{2}+4 x +1} \]
✓ Solution by Mathematica
Time used: 12.271 (sec). Leaf size: 19
DSolve[{y[x]*y''[x]+y'[x]^2+1==0,{y[0]==1,y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \sqrt {-x^2+4 x+1} \]