40.7.9 problem 18

Internal problem ID [6699]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 12. Linear equations of order n. Supplemetary problems. Page 81
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:24:22 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}&=2 \end{align*}

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 39

dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^2=2,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-2 c_1 x +2 x^{2}+2 c_2} \\ y &= -\sqrt {-2 c_1 x +2 x^{2}+2 c_2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 6.298 (sec). Leaf size: 101

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

\begin{align*} y(x)\to -\frac {\sqrt {4 (x+c_2){}^2-e^{2 c_1}}}{\sqrt {2}} \\ y(x)\to \sqrt {2 (x+c_2){}^2-\frac {e^{2 c_1}}{2}} \\ y(x)\to -\sqrt {2} \sqrt {(x+c_2){}^2} \\ y(x)\to \sqrt {2} \sqrt {(x+c_2){}^2} \\ \end{align*}