7.5.43 problem 43

Internal problem ID [147]
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 : 43
Date solved : Friday, February 07, 2025 at 07:58:37 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 11

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

\[ y = c_2 \,x^{2}+c_1 \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 17

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

\[ y(x)\to \frac {c_1 x^2}{2}+c_2 \]