Internal problem ID [15439]
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 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 674.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-2 x \right ) y^{\prime \prime }+\left (-x^{2}+2\right ) y^{\prime }-2 \left (1-x \right ) y=2 x -2} \] With initial conditions \begin {align*} [y \left (\infty \right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 13
dsolve([(x^2-2*x)*diff(y(x),x$2)+(2-x^2)*diff(y(x),x)-2*(1-x)*y(x)=2*(x-1),y(infinity) = 1],y(x), singsol=all)
\[ y \left (x \right ) = -\operatorname {signum}\left (c_{1} x^{2}\right ) \infty \]
✓ Solution by Mathematica
Time used: 0.314 (sec). Leaf size: 6
DSolve[{(x^2-2*x)*y''[x]+(2-x^2)*y'[x]-2*(1-x)*y[x]==2*(x-1),{y[Infinity]==1}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 1 \]