Internal problem ID [15400]
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: 631.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x^{2} y^{\prime \prime }-2 x y^{\prime }-2 y=x^{2}-2 x +2} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = x^{\frac {3}{2}+\frac {\sqrt {17}}{2}} c_{2} +x^{\frac {3}{2}-\frac {\sqrt {17}}{2}} c_{1} -\frac {x^{2}}{4}+\frac {x}{2}-1 \]
✓ Solution by Mathematica
Time used: 0.398 (sec). Leaf size: 53
DSolve[x^2*y''[x]-2*x*y'[x]-2*y[x]==x^2-2*x+2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 x^{\frac {1}{2} \left (3+\sqrt {17}\right )}+c_1 x^{\frac {3}{2}-\frac {\sqrt {17}}{2}}-\frac {x^2}{4}+\frac {x}{2}-1 \]