7.5.47 problem 47

Internal problem ID [151]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.6 (substitution and exact equations). Problems at page 72
Problem number : 47
Date solved : Friday, February 07, 2025 at 07:58:48 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 15

dsolve(diff(y(x),x$2)=diff(y(x),x)^2,y(x), singsol=all)
 

\[ y = -\ln \left (-c_1 x -c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.180 (sec). Leaf size: 15

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

\[ y(x)\to c_2-\log (x+c_1) \]