2.52 problem Problem 19(e)

Internal problem ID [10925]

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).
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\[ \boxed {\left (1-y\right ) y^{\prime \prime }-{y^{\prime }}^{2}=0} \]

Solution by Maple

Time used: 0.016 (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 \left (x \right ) = 1 \\ y \left (x \right ) = 1-\sqrt {2 c_{1} x +2 c_{2} +1} \\ y \left (x \right ) = 1+\sqrt {2 c_{1} x +2 c_{2} +1} \\ \end{align*}

Solution by Mathematica

Time used: 0.12 (sec). Leaf size: 43

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

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