67.2.52 problem Problem 19(e)

Internal problem ID [14009]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 19(e)
Date solved : Tuesday, January 28, 2025 at 06:12:29 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} \left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.055 (sec). Leaf size: 39

dsolve((1-y(x))*diff(y(x),x$2)-diff(y(x),x)^2=0,y(x), singsol=all)
 

\begin{align*} y &= 1 \\ y &= 1-\sqrt {2 c_{1} x +2 c_{2} +1} \\ y &= 1+\sqrt {2 c_{1} x +2 c_{2} +1} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.563 (sec). Leaf size: 49

DSolve[(1-y[x])*D[y[x],{x,2}]- D[y[x],x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to 1-\sqrt {-2 c_1 x+1-2 c_2 c_1} \\ y(x)\to 1+\sqrt {-2 c_1 x+1-2 c_2 c_1} \\ \end{align*}