15.18.21 problem 21

Internal problem ID [3264]
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 : 21
Date solved : Monday, January 27, 2025 at 07:29:42 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 33

dsolve(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 ) &= \sqrt {2 c_{1} x +2 c_{2}} \\ y \left (x \right ) &= -\sqrt {2 c_{1} x +2 c_{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.176 (sec). Leaf size: 20

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

\[ y(x)\to c_2 \sqrt {2 x-c_1} \]