Internal problem ID [13486]
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 (h).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]
\[ \boxed {\left (y-3\right ) y^{\prime \prime }-2 {y^{\prime }}^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 25
dsolve((y(x)-3)*diff(y(x),x$2)=2*diff(y(x),x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= 3 \\ y \left (x \right ) &= \frac {3 c_{1} x +3 c_{2} -1}{c_{1} x +c_{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.183 (sec). Leaf size: 44
DSolve[(y[x]-3)*y''[x]==2*y'[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3 c_1 x-1+3 c_2 c_1}{c_1 (x+c_2)} \\ y(x)\to 3 \\ y(x)\to \text {Indeterminate} \\ y(x)\to 3 \\ \end{align*}