Internal problem ID [14751]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {9 x^{2} y^{\prime \prime }+27 y^{\prime } x +10 y=\frac {1}{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 0, y^{\prime }\left (1\right ) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (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)
\[ y \left (x \right ) = \frac {-3 \sin \left (\frac {\ln \left (x \right )}{3}\right )-\cos \left (\frac {\ln \left (x \right )}{3}\right )+1}{x} \]
✓ Solution by Mathematica
Time used: 0.129 (sec). Leaf size: 28
DSolve[{9*x^2*y''[x]+27*x*y'[x]+10*y[x]==1/x,{y[1]==0,y'[1]==-1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3 \sin \left (\frac {\log (x)}{3}\right )+\cos \left (\frac {\log (x)}{3}\right )-1}{x} \]