Internal problem ID [15392]
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: 623.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+2 x \right )^{2} y^{\prime \prime }-2 \left (1+2 x \right ) y^{\prime }+4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = \frac {\left (2 x +1\right ) \left (-c_{2} \ln \left (2\right )+c_{2} \ln \left (2 x +1\right )+c_{1} \right )}{2} \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 23
DSolve[(2*x+1)^2*y''[x]-2*(2*x+1)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (2 x+1) (c_2 \log (2 x+1)+c_1) \]