Internal problem ID [15403]
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: 634.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {\left (x +1\right )^{3} y^{\prime \prime }+3 \left (x +1\right )^{2} y^{\prime }+\left (x +1\right ) y=6 \ln \left (x +1\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve((x+1)^3*diff(y(x),x$2)+3*(x+1)^2*diff(y(x),x)+(x+1)*y(x)=6*ln(x+1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} \ln \left (1+x \right )+\ln \left (1+x \right )^{3}+c_{2}}{1+x} \]
✓ Solution by Mathematica
Time used: 0.038 (sec). Leaf size: 27
DSolve[(x+1)^3*y''[x]+3*(x+1)^2*y'[x]+(x+1)*y[x]==6*Log[x+1],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {\log ^3(x+1)+c_2 \log (x+1)+c_1}{x+1} \]