Internal problem ID [2189]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/(1-x)^2,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (-1+c_{1} x -\ln \left (x -1\right )+c_{2} \right ) \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 23
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^x (-\log (x-1)+c_2 x-1+c_1) \]