Internal problem ID [11727]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.1. Basic theory of linear differential equations. Exercises page
124
Problem number: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x +1\right ) y^{\prime \prime }-4 \left (1+x \right ) y^{\prime }+4 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= {\mathrm e}^{2 x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([(2*x+1)*diff(y(x),x$2)-4*(x+1)*diff(y(x),x)+4*y(x)=0,exp(2*x)],singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+c_{1} x +c_{1} \]
✓ Solution by Mathematica
Time used: 0.125 (sec). Leaf size: 23
DSolve[(2*x+1)*y''[x]-4*(x+1)*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{2 x+1}-c_2 (x+1) \]