Internal problem ID [12759]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime } x^{2}+y^{\prime } x -4 y=-3 x -\frac {3}{x}} \] With initial conditions \begin {align*} [y \left (1\right ) = 3, y^{\prime }\left (1\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.015 (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)
\[ y \left (x \right ) = \frac {-x^{4}+x^{3}+x +2}{x^{2}} \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 20
DSolve[{x^2*y''[x]+x*y'[x]-4*y[x]==-3*x-3/x,{y[1]==3,y'[1]==-6}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-x^4+x^3+x+2}{x^2} \]