15.18.24 problem 24

Internal problem ID [3267]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 35, page 157
Problem number : 24
Date solved : Monday, January 27, 2025 at 07:29:48 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: 0.022 (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 \left (x \right ) &= 0 \\ y \left (x \right ) &= \sqrt {2 \,{\mathrm e}^{x} c_{1} +2 c_{2}} \\ y \left (x \right ) &= -\sqrt {2 \,{\mathrm e}^{x} c_{1} +2 c_{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.763 (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*}