Internal problem ID [10311]
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]]
Solve \begin {gather*} \boxed {\left (x -1\right )^{2} y^{\prime \prime }+4 \left (x -1\right ) y^{\prime }+2 y-\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 29
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)
\[ y \relax (x ) = \frac {c_{1} x}{\left (x -1\right )^{2}}-\frac {\cos \relax (x )}{\left (x -1\right )^{2}}+\frac {c_{2}}{\left (x -1\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.029 (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]
\begin{align*} y(x)\to \frac {-\cos (x)+c_1 (x-1)+c_2}{(x-1)^2} \\ \end{align*}