73.8.32 problem 13.5 (h)

Internal problem ID [15240]
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 (h)
Date solved : Tuesday, January 28, 2025 at 07:50:39 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (y-3\right ) y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

✓ Solution by Maple

Time used: 0.046 (sec). Leaf size: 16

dsolve((y(x)-3)*diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
 

\begin{align*} y &= 3 \\ y &= {\mathrm e}^{c_{1} x} c_{2} +3 \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.577 (sec). Leaf size: 16

DSolve[(y[x]-3)*D[y[x],{x,2}]==D[y[x],x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 3+e^{c_1 (x+c_2)} \]