73.8.35 problem 13.6 (a)

Internal problem ID [15243]
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 (a)
Date solved : Tuesday, January 28, 2025 at 07:50:43 AM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} x y^{\prime \prime }+4 y^{\prime }&=18 x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=8\\ y^{\prime }\left (1\right )&=-3 \end{align*}

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 14

dsolve([x*diff(y(x),x$2)+4*diff(y(x),x)=18*x^2,y(1) = 8, D(y)(1) = -3],y(x), singsol=all)
 

\[ y = x^{3}+\frac {2}{x^{3}}+5 \]

✓ Solution by Mathematica

Time used: 0.055 (sec). Leaf size: 15

DSolve[{x*D[y[x],{x,2}]+4*D[y[x],x]==18*x^2,{y[1]==8,Derivative[1][y][1]==-3}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x^3+\frac {2}{x^3}+5 \]