71.9.16 problem 18

Internal problem ID [14495]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 18
Date solved : Tuesday, January 28, 2025 at 06:42:36 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-4 y&=-3 x -\frac {3}{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=-6 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 19

dsolve([x^2*diff(y(x),x$2)+x*diff(y(x),x)-4*y(x)=-3*x-3/x,y(1) = 3, D(y)(1) = -6],y(x), singsol=all)
 

\[ y = \frac {-x^{4}+x^{3}+x +2}{x^{2}} \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 20

DSolve[{x^2*D[y[x],{x,2}]+x*D[y[x],x]-4*y[x]==-3*x-3/x,{y[1]==3,Derivative[1][y][1]==-6}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-x^4+x^3+x+2}{x^2} \]