Internal problem ID [1186]
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: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {\left (x -1\right )^{2} y^{\prime \prime }-\left (x^{2}-1\right ) y^{\prime }+\left (x -1\right )^{3} y-\left (x -1\right )^{3} {\mathrm e}^{x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 4, y^{\prime }\relax (0) = -6] \end {align*}
✗ Solution by Maple
dsolve([(x-1)^2*diff(y(x),x$2)-(x^2-1)*diff(y(x),x)+(x-1)^3*y(x)=(x-1)^3*exp(x),y(0) = 4, D(y)(0) = -6],y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[{(x-1)^2*y''[x]-(x^2-1)*y'[x]+(x-1)^3*y[x]==(x-1)^3*Exp[x],{y[0]==4,y'[0]==-6}},y[x],x,IncludeSingularSolutions -> True]
Not solved