62.28.3 problem Ex 3

Internal problem ID [12950]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter VII, Linear differential equations with constant coefficients. Article 51. Cauchy linear equation. Page 114
Problem number : Ex 3
Date solved : Tuesday, January 28, 2025 at 04:44:52 AM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+3 x y^{\prime }+y&=\frac {1}{\left (1-x \right )^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 22

dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=1/(1-x)^2,y(x), singsol=all)
 

\[ y = \frac {\ln \left (x \right ) c_{1} +\ln \left (x \right )-\ln \left (x -1\right )+c_{2}}{x} \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 27

DSolve[x^2*D[y[x],{x,2}]+3*x*D[y[x],x]+y[x]==1/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-\log (1-x)+\log (x)+c_2 \log (x)+c_1}{x} \]