15.12.16 problem 16

Internal problem ID [3160]
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
Date solved : Monday, January 27, 2025 at 07:24:10 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+y&=\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = {\mathrm e}^{x} \left (-1+c_{1} x -\ln \left (x -1\right )+c_2 \right ) \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 23

DSolve[D[y[x],{x,2}]-2*D[y[x],x]+y[x]==Exp[x]/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x (-\log (x-1)+c_2 x-1+c_1) \]