73.16.15 problem 24.2 (a)

Internal problem ID [15527]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 24. Variation of parameters. Additional exercises page 444
Problem number : 24.2 (a)
Date solved : Tuesday, January 28, 2025 at 08:01:17 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-4 y&=\frac {10}{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=3\\ y^{\prime }\left (1\right )&=-15 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 19

dsolve([x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-4*y(x)=10/x,y(1) = 3, D(y)(1) = -15],y(x), singsol=all)
 

\[ y = \frac {-2 x^{5}-2 \ln \left (x \right )+5}{x} \]

✓ Solution by Mathematica

Time used: 0.018 (sec). Leaf size: 20

DSolve[{x^2*D[y[x],{x,2}]-2*x*D[y[x],x]-4*y[x]==10/x,{y[1]==3,Derivative[1][y][1]==-15}},y[x],x,IncludeSingularSolutions -> True]
 

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