Internal problem ID [13480]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 13. Higher order equations: Extending first order concepts. Additional exercises
page 259
Problem number: 13.2 (b).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], [_2nd_order, _reducible, _mu_poly_yn]]
\[ \boxed {y^{\prime } y^{\prime \prime }=1} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 40
dsolve(diff(y(x),x)*diff(y(x),x$2)=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\left (2 x +2 c_{1} \right )^{\frac {3}{2}}}{3}+c_{2} \\ y \left (x \right ) &= \frac {\left (-2 c_{1} -2 x \right ) \sqrt {2 x +2 c_{1}}}{3}+c_{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 49
DSolve[y'[x]*y''[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {2}{3} \sqrt {2} (x+c_1){}^{3/2} \\ y(x)\to \frac {2}{3} \sqrt {2} (x+c_1){}^{3/2}+c_2 \\ \end{align*}