Internal problem ID [11325]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 60. Exact equation. Integrating factor. Page 139
Problem number: Ex 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y=\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 19
dsolve((x-1)^2*diff(y(x),x$2)+4*(x-1)*diff(y(x),x)+2*y(x)=cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} +c_{1} x -\cos \left (x \right )}{\left (-1+x \right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 24
DSolve[(x-1)^2*y''[x]+4*(x-1)*y'[x]+2*y[x]==Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {-\cos (x)+c_1 (x-1)+c_2}{(x-1)^2} \]