71.9.10 problem 10

Internal problem ID [14489]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 10
Date solved : Tuesday, January 28, 2025 at 06:42:22 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 2 y y^{\prime \prime }-{y^{\prime }}^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.066 (sec). Leaf size: 17

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

\begin{align*} y &= 0 \\ y &= \frac {\left (c_{1} x +c_{2} \right )^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 29

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

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