75.19.18 problem 635

Internal problem ID [17134]
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 ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 635
Date solved : Tuesday, January 28, 2025 at 09:53:59 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x -2\right )^{2} y^{\prime \prime }-3 \left (x -2\right ) y^{\prime }+4 y&=x \end{align*}

✓ Solution by Maple

Time used: 0.005 (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)
 

\[ y = \left (x -2\right )^{2} c_{2} +\left (x -2\right )^{2} \ln \left (x -2\right ) c_{1} +x -\frac {3}{2} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 31

DSolve[(x-2)^2*D[y[x],{x,2}]-3*(x-2)*D[y[x],x]+4*y[x]==x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to x+c_1 (x-2)^2+2 c_2 (x-2)^2 \log (x-2)-\frac {3}{2} \]