75.19.6 problem 623

Internal problem ID [17122]
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 : 623
Date solved : Tuesday, January 28, 2025 at 09:53:37 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right )^{2} y^{\prime \prime }-2 \left (2 x +1\right ) y^{\prime }+4 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

dsolve((2*x+1)^2*diff(y(x),x$2)-2*(2*x+1)*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 23

DSolve[(2*x+1)^2*D[y[x],{x,2}]-2*(2*x+1)*D[y[x],x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (2 x+1) (c_2 \log (2 x+1)+c_1) \]