Internal problem ID [11274]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+3 y^{\prime } x +y=\frac {1}{\left (1-x \right )^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {c_{1} \ln \left (x \right )-\ln \left (-1+x \right )+\ln \left (x \right )+c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 27
DSolve[x^2*y''[x]+3*x*y'[x]+y[x]==1/(1-x)^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\log (1-x)+\log (x)+c_2 \log (x)+c_1}{x} \]