73.8.47 problem 13.8 (ii)

Internal problem ID [15255]
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 : 13.8 (ii)
Date solved : Tuesday, January 28, 2025 at 07:51:00 AM
CAS classification : [[_2nd_order, _missing_y], [_2nd_order, _reducible, _mu_y_y1]]

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

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 5

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

\[ y = 3 \]

✓ Solution by Mathematica

Time used: 23.378 (sec). Leaf size: 6

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

\[ y(x)\to 3 \]