50.7.5 problem 1(e)

Internal problem ID [7909]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.9. Reduction of Order. Page 38
Problem number : 1(e)
Date solved : Monday, January 27, 2025 at 03:31:52 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _reducible, _mu_x_y1]]

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

✓ Solution by Maple

Time used: 0.029 (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: 0.026 (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*}