73.8.28 problem 13.5 (d)

Internal problem ID [15236]
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 : 13.5 (d)
Date solved : Tuesday, January 28, 2025 at 07:50:36 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

\begin{align*} x y^{\prime \prime }&={y^{\prime }}^{2}-y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.033 (sec). Leaf size: 17

dsolve(x*diff(y(x),x$2)=diff(y(x),x)^2-diff(y(x),x),y(x), singsol=all)
 

\[ y = -\frac {\ln \left (c_{1} x -1\right )}{c_{1}}+c_{2} \]

✓ Solution by Mathematica

Time used: 1.067 (sec). Leaf size: 42

DSolve[x*D[y[x],{x,2}]==D[y[x],x]^2-D[y[x],x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][c_1+\log (K[2])]dK[2]+c_2 \]