Internal problem ID [10256]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +y-\frac {1}{\left (1-x \right )^{2}}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(x^2*diff(y(x),x$2)+3*x*diff(y(x),x)+y(x)=1/(1-x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\ln \left (x \right ) c_{1}}{x}+\frac {c_{2}}{x}-\frac {\ln \left (x -1\right )-\ln \left (x \right )}{x} \]
✓ Solution by Mathematica
Time used: 0.016 (sec). Leaf size: 25
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==1/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {-2 \text {arctanh}(1-2 x)+c_2 \log (x)+c_1}{x} \\ \end{align*}