73.8.43 problem 13.7 (c)

Internal problem ID [15251]
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 : 13.7 (c)
Date solved : Tuesday, January 28, 2025 at 07:50:55 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 (1\right )&=1\\ y^{\prime }\left (1\right )&=9 \end{align*}

✓ Solution by Maple

Time used: 0.052 (sec). Leaf size: 11

dsolve([3*y(x)*diff(y(x),x$2)=2*diff(y(x),x)^2,y(1) = 1, D(y)(1) = 9],y(x), singsol=all)
 

\[ y = \left (3 x -2\right )^{3} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 12

DSolve[{3*y[x]*D[y[x],{x,2}]==2*D[y[x],x]^2,{y[1]==1,Derivative[1][y][1]==9}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (3 x-2)^3 \]