75.20.1 problem 636

Internal problem ID [17135]
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 15.5 Linear equations with variable coefficients. The Lagrange method. Exercises page 148
Problem number : 636
Date solved : Tuesday, January 28, 2025 at 09:54:00 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x +1\right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 18

dsolve((2*x+1)*diff(y(x),x$2)+(4*x-2)*diff(y(x),x)-8*y(x)=0,y(x), singsol=all)
 

\[ y = 4 c_{1} x^{2}+c_{2} {\mathrm e}^{-2 x}+c_{1} \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 92

DSolve[(2*x+1)*D[y[x],{x,2}]+(4*x-2)*D[y[x],x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \exp \left (\int _1^x\left (-1-\frac {2}{2 K[1]+1}\right )dK[1]-\frac {1}{2} \int _1^x\left (2-\frac {4}{2 K[2]+1}\right )dK[2]\right ) \left (c_2 \int _1^x\exp \left (-2 \int _1^{K[3]}-\frac {2 K[1]+3}{2 K[1]+1}dK[1]\right )dK[3]+c_1\right ) \]