Internal problem ID [15404]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.4 Nonhomogeneous linear equations with
constant coefficients. The Euler equations. Exercises page 143
Problem number: 635.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y=x} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 25
dsolve((x-2)^2*diff(y(x),x$2)-3*(x-2)*diff(y(x),x)+4*y(x)=x,y(x), singsol=all)
\[ y \left (x \right ) = \left (x -2\right )^{2} c_{2} +\left (x -2\right )^{2} \ln \left (x -2\right ) c_{1} +x -\frac {3}{2} \]
✓ Solution by Mathematica
Time used: 0.061 (sec). Leaf size: 31
DSolve[(x-2)^2*y''[x]-3*(x-2)*y'[x]+4*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x+c_1 (x-2)^2+2 c_2 (x-2)^2 \log (x-2)-\frac {3}{2} \]