Internal problem ID [5356]
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.
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]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{2}=2} \]
✓ Solution by Maple
Time used: 0.016 (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 \left (x \right ) &= \sqrt {-2 c_{1} x +2 x^{2}+2 c_{2}} \\ y \left (x \right ) &= -\sqrt {-2 c_{1} x +2 x^{2}+2 c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.295 (sec). Leaf size: 101
DSolve[y[x]*y''[x]+y'[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*}