7.5.49 problem 49

Internal problem ID [153]
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 : 49
Date solved : Friday, February 07, 2025 at 07:58:51 AM
CAS classification : [[_2nd_order, _missing_x], [_2nd_order, _exact, _nonlinear], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

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

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 35

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

\begin{align*} y &= 0 \\ y &= \sqrt {2 c_1 \,{\mathrm e}^{x}+2 c_2} \\ y &= -\sqrt {2 c_1 \,{\mathrm e}^{x}+2 c_2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.778 (sec). Leaf size: 41

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

\begin{align*} y(x)\to c_2 \sqrt {2 e^x+e^{c_1}} \\ y(x)\to \sqrt {2} c_2 \sqrt {e^x} \\ \end{align*}