Internal problem ID [15184]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 13. Basic concepts and definitions. Exercises
page 98
Problem number: 326.
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]]
\[ \boxed {{y^{\prime }}^{2}+y y^{\prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(diff(y(x),x)^2+y(x)*diff(y(x),x$2)=1,y(x), singsol=all)
\begin{align*} y &= \sqrt {-2 c_{1} x +x^{2}+2 c_{2}} \\ y &= -\sqrt {-2 c_{1} x +x^{2}+2 c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.593 (sec). Leaf size: 79
DSolve[y'[x]^2+y[x]*y''[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {(x+c_2){}^2-e^{2 c_1}} \\ y(x)\to \sqrt {(x+c_2){}^2-e^{2 c_1}} \\ y(x)\to -\sqrt {(x+c_2){}^2} \\ y(x)\to \sqrt {(x+c_2){}^2} \\ \end{align*}