Internal problem ID [10238]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 47. Particular
integral. Page 100
Problem number: Ex 4.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y-\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/(1-x)^2,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}+{\mathrm e}^{x} c_{1} x +{\mathrm e}^{x} \left (-1-\ln \left (x -1\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.012 (sec). Leaf size: 23
DSolve[y''[x]-2*y'[x]+y[x]==Exp[x]/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^x (-\log (x-1)+c_2 x-1+c_1) \\ \end{align*}