Internal problem ID [15399]
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: 630.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }-x y^{\prime }-3 y=-\frac {16 \ln \left (x \right )}{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(x^2*diff(y(x),x$2)-x*diff(y(x),x)-3*y(x)=-16*ln(x)/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {4 c_{2} x^{4}+8 \ln \left (x \right )^{2}+4 \ln \left (x \right )+4 c_{1} +1}{4 x} \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 35
DSolve[x^2*y''[x]-x*y'[x]-3*y[x]==-16*Log[x]/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {4 c_2 x^4+8 \log ^2(x)+4 \log (x)+1+4 c_1}{4 x} \]