8.28 problem 28

Internal problem ID [4383]

Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section: Chapter 8, Ordinary differential equations. Section 13. Miscellaneous problems. page 466
Problem number: 28.
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]]

Solve \begin {gather*} \boxed {y y^{\prime \prime }+\left (y^{\prime }\right )^{2}+4=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 3, y^{\prime }\relax (1) = 0] \end {align*}

Solution by Maple

Time used: 0.448 (sec). Leaf size: 16

dsolve([y(x)*diff(y(x),x$2)+diff(y(x),x)^2+4=0,y(1) = 3, D(y)(1) = 0],y(x), singsol=all)
 

\[ y \relax (x ) = \sqrt {-4 x^{2}+8 x +5} \]

Solution by Mathematica

Time used: 0.16 (sec). Leaf size: 17

DSolve[{y[x]*y''[x]+y'[x]^2+4==0,{y[1]==3,y'[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt {5-4 (x-2) x} \\ \end{align*}