82.44.1 problem Ex. 1

Internal problem ID [18965]
Book : Introductory Course On Differential Equations by Daniel A Murray. Longmans Green and Co. NY. 1924
Section : Chapter VIII. Exact differential equations, and equations of particular forms. Integration in series. problems at page 99
Problem number : Ex. 1
Date solved : Tuesday, January 28, 2025 at 12:40:57 PM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 18

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

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

✓ Solution by Mathematica

Time used: 0.217 (sec). Leaf size: 20

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

\[ y(x)\to c_2-\frac {\log (a x+c_1)}{a} \]