Internal problem ID [1185]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -1\right )^{2} y^{\prime \prime }-2 \left (x -1\right ) y^{\prime }+2 y-\left (x -1\right )^{2}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -6] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 33
dsolve([(x-1)^2*diff(y(x),x$2)-2*(x-1)*diff(y(x),x)+2*y(x)=(x-1)^2,y(0) = 3, D(y)(0) = -6],y(x), singsol=all)
\[ y \left (x \right ) = -\left (x -1\right ) \left (i \pi x -i \pi -\ln \left (x -1\right ) x +\ln \left (x -1\right )-2 x +3\right ) \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 30
DSolve[{(x-1)^2*y''[x]-2*(x-1)*y'[x]+2*y[x]==(x-1)^2,{y[0]==3,y'[0]==-6}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x-1) (-i \pi (x-1)+2 x+(x-1) \log (x-1)-3) \\ \end{align*}