75.22.5 problem 710

Internal problem ID [17184]
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 17. Boundary value problems. Exercises page 163
Problem number : 710
Date solved : Tuesday, January 28, 2025 at 09:56:28 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} y y^{\prime \prime }+{y^{\prime }}^{2}+1&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 4.150 (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)
 

\[ y = \sqrt {-x^{2}+4 x +1} \]

✓ Solution by Mathematica

Time used: 11.627 (sec). Leaf size: 19

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

\[ y(x)\to \sqrt {-x^2+4 x+1} \]