Internal problem ID [13545]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 14. Higher order equations and the reduction of order method. Additional
exercises page 277
Problem number: 14.2 (j).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {x y^{\prime \prime }+\left (2 x +2\right ) y^{\prime }+2 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= \frac {1}{x} \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
dsolve([x*diff(y(x),x$2)+(2+2*x)*diff(y(x),x)+2*y(x)=0,1/x],singsol=all)
\[ y \left (x \right ) = \frac {c_{1} +{\mathrm e}^{-2 x} c_{2}}{x} \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 24
DSolve[x*y''[x]+(2+2*x)*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {2 c_1 e^{-2 x}+c_2}{2 x} \]