Internal problem ID [1187]
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: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x -1\right )^{2} y^{\prime \prime }+4 y^{\prime } x +2 y-2 x=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 0, y^{\prime }\relax (0) = -2] \end {align*}
✓ Solution by Maple
Time used: 0.093 (sec). Leaf size: 61
dsolve([(x-1)^2*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=2*x,y(0) = 0, D(y)(0) = -2],y(x), singsol=all)
\[ y \relax (x ) = \frac {\left (-28 \expIntegral \left (1, -4\right )+28 \expIntegral \left (1, \frac {4}{x -1}\right )\right ) {\mathrm e}^{\frac {4}{x -1}}+x^{3}-2 x^{2}-6 x -7 \,{\mathrm e}^{\frac {4 x}{x -1}}+7}{3 \left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 70
DSolve[{(x-1)^2*y''[x]+4*x*y'[x]+2*y[x]==2*x,{y[0]==0,y'[0]==-2}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-28 e^{\frac {4}{x-1}} \text {Ei}\left (-\frac {4}{x-1}\right )+28 \text {Ei}(4) e^{\frac {4}{x-1}}+(x-1) ((x-1) x-7)-7 e^{\frac {4 x}{x-1}}}{3 (x-1)^2} \\ \end{align*}