Internal problem ID [7706]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 219.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {f^{\prime \prime }+2 \left (z -1\right ) f^{\prime }+4 f=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 74
dsolve(diff(f(z),z$2)+2*(z-1)*diff(f(z),z)+4*f(z)=0,f(z), singsol=all)
\[ f \left (z \right ) = c_{1} {\mathrm e}^{-z^{2}+2 z} \left (z -1\right )+c_{2} {\mathrm e}^{-z^{2}+2 z} \left (-{\mathrm e}^{-1} \sqrt {\pi }\, \operatorname {erf}\left (i z -i\right ) z +{\mathrm e}^{-1} \sqrt {\pi }\, \operatorname {erf}\left (i z -i\right )+i {\mathrm e}^{z^{2}-2 z}\right ) \]
✓ Solution by Mathematica
Time used: 0.176 (sec). Leaf size: 72
DSolve[f''[z]+2*(z-a)*f'[z]+4*f[z]==0,f[z],z,IncludeSingularSolutions -> True]
\[ f(z)\to e^{z (2 a-z)} \left (-\sqrt {\pi } c_2 \sqrt {(a-z)^2} \text {erfi}\left (\sqrt {(a-z)^2}\right )+c_2 e^{(a-z)^2}-2 a c_1+2 c_1 z\right ) \]