75.19.14 problem 631

Internal problem ID [17130]
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 : 631
Date solved : Tuesday, January 28, 2025 at 09:53:49 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y&=x^{2}-2 x +2 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 36

dsolve(x^2*diff(y(x),x$2)-2*x*diff(y(x),x)-2*y(x)=x^2-2*x+2,y(x), singsol=all)
 

\[ y = x^{\frac {3}{2}+\frac {\sqrt {17}}{2}} c_{2} +x^{\frac {3}{2}-\frac {\sqrt {17}}{2}} c_{1} -\frac {x^{2}}{4}+\frac {x}{2}-1 \]

✓ Solution by Mathematica

Time used: 0.436 (sec). Leaf size: 53

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

\[ y(x)\to c_2 x^{\frac {1}{2} \left (3+\sqrt {17}\right )}+c_1 x^{\frac {3}{2}-\frac {\sqrt {17}}{2}}-\frac {x^2}{4}+\frac {x}{2}-1 \]