15.18.25 problem 25

Internal problem ID [3268]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 25
Date solved : Monday, January 27, 2025 at 07:29:49 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: 0.019 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= \frac {\left (c_{1} x +c_{2} \right )^{2}}{4} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.019 (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*}