Internal problem ID [7372]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 653.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f=0} \end {gather*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 45
dsolve(diff(f(z),z$2)+2*(z-1)*diff(f(z),z)+4*f(z)=0,f(z), singsol=all)
\[ f \relax (z ) = c_{1} {\mathrm e}^{-z \left (z -2\right )} \left (z -1\right )+c_{2} \left (-\sqrt {\pi }\, \erf \left (i \left (z -1\right )\right ) \left (z -1\right ) {\mathrm e}^{-\left (z -1\right )^{2}}+i\right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 56
DSolve[f''[z]+2*(z-a)*f'[z]+4*f[z]==0,f[z],z,IncludeSingularSolutions -> True]
\begin{align*} f(z)\to e^{z (2 a-z)} \left (c_2 e^{(a-z)^2}-(a-z) \left (\sqrt {\pi } c_2 \operatorname {Erfi}(a-z)+2 c_1\right )\right ) \\ \end{align*}