Internal problem ID [15401]
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: 632.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-y=x^{m}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=x^m,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} x +\frac {x^{m}}{\left (m -1\right ) \left (m +1\right )} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 27
DSolve[x^2*y''[x]+x*y'[x]-y[x]==x^m,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^m}{m^2-1}+c_2 x+\frac {c_1}{x} \]