75.19.17 problem 634

Internal problem ID [17133]
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 ODEs). Section 15.4 Nonhomogeneous linear equations with constant coefficients. The Euler equations. Exercises page 143
Problem number : 634
Date solved : Tuesday, January 28, 2025 at 09:53:57 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (1+x \right )^{3} y^{\prime \prime }+3 \left (1+x \right )^{2} y^{\prime }+\left (1+x \right ) y&=6 \ln \left (1+x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (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)
 

\[ y = \frac {c_{1} \ln \left (x +1\right )+\ln \left (x +1\right )^{3}+c_{2}}{x +1} \]

✓ Solution by Mathematica

Time used: 0.036 (sec). Leaf size: 27

DSolve[(x+1)^3*D[y[x],{x,2}]+3*(x+1)^2*D[y[x],x]+(x+1)*y[x]==6*Log[x+1],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\log ^3(x+1)+c_2 \log (x+1)+c_1}{x+1} \]