73.8.36 problem 13.6 (b)

Internal problem ID [15244]
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 : 13.6 (b)
Date solved : Tuesday, January 28, 2025 at 07:50:45 AM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (-1\right )&=4\\ y^{\prime }\left (-1\right )&=12 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 11

dsolve([x*diff(y(x),x$2)=2*diff(y(x),x),y(-1) = 4, D(y)(-1) = 12],y(x), singsol=all)
 

\[ y = 4 x^{3}+8 \]

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 12

DSolve[{x*D[y[x],{x,2}]==2*D[y[x],x],{y[-1]==4,Derivative[1][y][-1]==12}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 4 \left (x^3+2\right ) \]