73.8.20 problem 13.4 (a)

Internal problem ID [15228]
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 (a)
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*} y y^{\prime \prime }&={y^{\prime }}^{2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=5\\ y^{\prime }\left (0\right )&=15 \end{align*}

✓ Solution by Maple

Time used: 0.141 (sec). Leaf size: 10

dsolve([y(x)*diff(y(x),x$2)=diff(y(x),x)^2,y(0) = 5, D(y)(0) = 15],y(x), singsol=all)
 

\[ y = 5 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.105 (sec). Leaf size: 12

DSolve[{y[x]*D[y[x],{x,2}]==D[y[x],x]^2,{y[0]==5,Derivative[1][y][0] ==15}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 5 e^{3 x} \]