81.7.5 problem 6

Internal problem ID [18702]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter VI. Certain particular forms of equations. Exercises at page 74
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 12:11:59 PM
CAS classification : [[_2nd_order, _missing_x], _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: 0.014 (sec). Leaf size: 14

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 ) &= {\mathrm e}^{c_{1} x} c_{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.113 (sec). Leaf size: 14

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

\[ y(x)\to c_2 e^{c_1 x} \]