Internal problem ID [5434]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {y y^{\prime \prime }+{y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(y(x)*diff(y(x),x$2)+diff(y(x),x)^2=0,y(x), singsol=all)
\begin{align*} y = 0 y = \sqrt {2 c_{1} x +2 c_{2}} y = -\sqrt {2 c_{1} x +2 c_{2}} \end{align*}
✓ Solution by Mathematica
Time used: 0.172 (sec). Leaf size: 20
DSolve[y[x]*y''[x]+y'[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 \sqrt {2 x-c_1} \]