35.8.28 problem 28

Internal problem ID [6235]
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
Date solved : Monday, January 27, 2025 at 01:49:41 PM
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}+4&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.739 (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)
 

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

✓ Solution by Mathematica

Time used: 33.073 (sec). Leaf size: 19

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

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