73.8.24 problem 13.4 (e)

Internal problem ID [15232]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 13. Higher order equations: Extending first order concepts. Additional exercises page 259
Problem number : 13.4 (e)
Date solved : Tuesday, January 28, 2025 at 07:50:30 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^{\prime }}^{2}+y y^{\prime \prime }&=2 y^{\prime } y \end{align*}

✓ Solution by Maple

Time used: 0.072 (sec). Leaf size: 37

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

\begin{align*} y &= 0 \\ y &= \sqrt {{\mathrm e}^{2 x} c_{1} +2 c_{2}} \\ y &= -\sqrt {{\mathrm e}^{2 x} c_{1} +2 c_{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.484 (sec). Leaf size: 45

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

\[ y(x)\to c_2 \exp \left (\int _1^x\text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{(K[1]-1) K[1]}dK[1]\&\right ][c_1-2 K[2]]dK[2]\right ) \]