74.15.42 problem 42

Internal problem ID [16481]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 42
Date solved : Tuesday, January 28, 2025 at 09:09:05 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} 9 x^{2} y^{\prime \prime }+27 x y^{\prime }+10 y&=\frac {1}{x} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0\\ y^{\prime }\left (1\right )&=-1 \end{align*}

✓ Solution by Maple

Time used: 0.030 (sec). Leaf size: 24

dsolve([9*x^2*diff(y(x),x$2)+27*x*diff(y(x),x)+10*y(x)=1/x,y(1) = 0, D(y)(1) = -1],y(x), singsol=all)
 

\[ y = \frac {-3 \sin \left (\frac {\ln \left (x \right )}{3}\right )-\cos \left (\frac {\ln \left (x \right )}{3}\right )+1}{x} \]

✓ Solution by Mathematica

Time used: 0.152 (sec). Leaf size: 81

DSolve[{9*x^2*D[y[x],{x,2}]+27*x*D[y[x],x]+10*y[x]==1/x,{y[1]==0,Derivative[1][y][1]==-1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sin \left (\frac {\log (x)}{3}\right ) \int _1^x\frac {\cos \left (\frac {1}{3} \log (K[1])\right )}{3 K[1]}dK[1]+\cos \left (\frac {\log (x)}{3}\right ) \int _1^x-\frac {\sin \left (\frac {1}{3} \log (K[2])\right )}{3 K[2]}dK[2]-3 \sin \left (\frac {\log (x)}{3}\right )}{x} \]