Internal problem ID [15396]
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: 627.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {\left (1+2 x \right )^{2} y^{\prime \prime \prime }+2 \left (1+2 x \right ) y^{\prime \prime }+y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve((2*x+1)^2*diff(y(x),x$3)+2*(2*x+1)*diff(y(x),x$2)+diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} +\frac {c_{2} \left (2 x +1\right ) \sin \left (-\frac {\ln \left (2\right )}{2}+\frac {\ln \left (2 x +1\right )}{2}\right )}{2}+\frac {c_{3} \left (2 x +1\right ) \cos \left (-\frac {\ln \left (2\right )}{2}+\frac {\ln \left (2 x +1\right )}{2}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.153 (sec). Leaf size: 58
DSolve[(2*x+1)^2*y'''[x]+2*(2*x+1)*y''[x]+y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{5} (2 x+1) \left ((2 c_1-c_2) \cos \left (\frac {1}{2} \log (2 x+1)\right )+(c_1+2 c_2) \sin \left (\frac {1}{2} \log (2 x+1)\right )\right )+c_3 \]