78.7.5 problem 1 (e)

Internal problem ID [18191]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 11 (Reduction of order). Problems at page 87
Problem number : 1 (e)
Date solved : Tuesday, January 28, 2025 at 11:37:40 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

\begin{align*} 2 y y^{\prime \prime }&={y^{\prime }}^{2}+1 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 22

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

\[ y = \frac {\left (c_{1}^{2}+1\right ) x^{2}}{4 c_{2}}+c_{1} x +c_{2} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 34

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

\begin{align*} y(x)\to \frac {\left (1+c_1{}^2\right ) x^2}{4 c_2}+c_1 x+c_2 \\ y(x)\to \text {Indeterminate} \\ \end{align*}