75.19.10 problem 627

Internal problem ID [17126]
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 : 627
Date solved : Tuesday, January 28, 2025 at 09:53:40 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (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)
 

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

✓ Solution by Mathematica

Time used: 60.038 (sec). Leaf size: 46

DSolve[(2*x+1)^2*D[y[x],{x,3}]+2*(2*x+1)*D[y[x],{x,2}]+D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \int _1^x\left (c_1 \cos \left (\frac {1}{2} \log (2 K[1]+1)\right )+c_2 \sin \left (\frac {1}{2} \log (2 K[1]+1)\right )\right )dK[1]+c_3 \]