How to solve $\frac{\mathrm{d}^4 y}{\mathrm{d} x^4}-2{\frac{\mathrm{d^3}y}{\mathrm{d} x^3}}+2{\frac{\mathrm{d^2}y }{\mathrm{d} x^2}}+y=0$? I tried to solve the equation 

$$\frac{\mathrm{d}^4 y}{\mathrm{d} x^4}-2{\frac{\mathrm{d^3}y}{\mathrm{d} x^3}}+2{\frac{\mathrm{d^2}y }{\mathrm{d} x}}+y=0$$

by writing its Auxiliary Equation

$$
m^{4}-2m^{3}+2m^{2}+1=0,
$$

But now I am unable to solve this polynomial.
One solution is given by $$m=1/2+1/6\,\sqrt {3}\sqrt {{\frac { \left( -10+6\,i\sqrt {111} \right) ^
{2/3}-\sqrt [3]{-10+6\,i\sqrt {111}}+16}{\sqrt [3]{-10+6\,i\sqrt {111}
}}}}+1/6\,\sqrt {-3\,{\frac { \left( -10+6\,i\sqrt {111} \right) ^{2/3
}\sqrt {{\frac { \left( -10+6\,i\sqrt {111} \right) ^{2/3}-\sqrt [3]{-
10+6\,i\sqrt {111}}+16}{\sqrt [3]{-10+6\,i\sqrt {111}}}}}+6\,\sqrt {3}
\sqrt [3]{-10+6\,i\sqrt {111}}+2\,\sqrt [3]{-10+6\,i\sqrt {111}}\sqrt 
{{\frac { \left( -10+6\,i\sqrt {111} \right) ^{2/3}-\sqrt [3]{-10+6\,i
\sqrt {111}}+16}{\sqrt [3]{-10+6\,i\sqrt {111}}}}}+16\,\sqrt {{\frac {
 \left( -10+6\,i\sqrt {111} \right) ^{2/3}-\sqrt [3]{-10+6\,i\sqrt {
111}}+16}{\sqrt [3]{-10+6\,i\sqrt {111}}}}}}{\sqrt [3]{-10+6\,i\sqrt {
111}}\sqrt {{\frac { \left( -10+6\,i\sqrt {111} \right) ^{2/3}-\sqrt [
3]{-10+6\,i\sqrt {111}}+16}{\sqrt [3]{-10+6\,i\sqrt {111}}}}}}}}
$$
go to wolfram alpha
https://www.wolframalpha.com/input/?i=complex+z+%3A++z%5E4%E2%88%922*z%5E3%2B2*z%5E2%2B1%3D0
if you don't want to use the awful formula