40.14.6 problem 27

Internal problem ID [6777]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary problems. Page 132
Problem number : 27
Date solved : Monday, January 27, 2025 at 02:30:17 PM
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: 0.010 (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 &= 0 \\ y &= \sqrt {2 c_1 x +2 c_2} \\ y &= -\sqrt {2 c_1 x +2 c_2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.167 (sec). Leaf size: 20

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

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