73.8.21 problem 13.4 (b)

Internal problem ID [15229]
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 (b)
Date solved : Tuesday, January 28, 2025 at 07:50:26 AM
CAS classification : [[_2nd_order, _missing_x], _Liouville, [_2nd_order, _reducible, _mu_x_y1], [_2nd_order, _reducible, _mu_xy]]

\begin{align*} 3 y y^{\prime \prime }&=2 {y^{\prime }}^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=8\\ y^{\prime }\left (0\right )&=6 \end{align*}

✓ Solution by Maple

Time used: 0.120 (sec). Leaf size: 11

dsolve([3*y(x)*diff(y(x),x$2)=2*diff(y(x),x)^2,y(0) = 8, D(y)(0) = 6],y(x), singsol=all)
 

\[ y = \frac {\left (x +4\right )^{3}}{8} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 14

DSolve[{3*y[x]*D[y[x],{x,2}]==2*D[y[x],x]^2,{y[0]==8,Derivative[1][y][0] ==6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} (x+4)^3 \]