Internal problem ID [15405]
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 15.5 Linear equations with variable coefficients.
The Lagrange method. Exercises page 148
Problem number: 636.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+2 x \right ) y^{\prime \prime }+\left (4 x -2\right ) y^{\prime }-8 y=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = 4 c_{1} x^{2}+c_{2} {\mathrm e}^{-2 x}+c_{1} \]
✓ Solution by Mathematica
Time used: 0.192 (sec). Leaf size: 27
DSolve[(2*x+1)*y''[x]+(4*x-2)*y'[x]-8*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} c_2 \left (4 x^2+1\right )+c_1 e^{-2 x} \]