81.2.1 problem 1

Internal problem ID [18609]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 12:04:01 PM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Lagerstrom, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 16

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

\[ y \left (x \right ) = \frac {\tan \left (\frac {c_{2} +x}{c_{1}}\right )}{c_{1}} \]

✓ Solution by Mathematica

Time used: 9.662 (sec). Leaf size: 24

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

\[ y(x)\to \sqrt {c_1} \tan \left (\sqrt {c_1} (x+c_2)\right ) \]