Internal problem ID [13162]
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 (d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]
\[ \boxed {x y^{\prime \prime }-{y^{\prime }}^{2}+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)=diff(y(x),x)^2-diff(y(x),x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\ln \left (c_{1} x -1\right )}{c_{1}}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.301 (sec). Leaf size: 38
DSolve[x*y''[x]==(y'[x])^2-y'[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{-c_1} \log \left (1+e^{c_1} x\right )+c_2 y(x)\to c_2 y(x)\to x+c_2 \end{align*}