24.4 problem Ex 4

Internal problem ID [10242]

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]]

Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }+y-\frac {{\mathrm e}^{x}}{\left (1-x \right )^{2}}=0} \end {gather*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 24

dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=exp(x)/(1-x)^2,y(x), singsol=all)
 

\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1}-\left (\ln \left (x -1\right )+1\right ) {\mathrm e}^{x} \]

Solution by Mathematica

Time used: 0.013 (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*}