I need some help / solutions for the following equations, where $M \ge 0 \in R$, $s \in C$, and $C_n$ are functions of $M$ only (stated further below)
Equation 1;
$$M+5\sqrt{M}+2=C_1s^{2\sqrt{M}+2}+C_2s^{2\sqrt{M}-2}+C_3s^2$$
Equation 2;
$$M-3\sqrt{M}+1=C_4s^{2\sqrt{M}+2}+C_5s^{\sqrt{M}+2}+C_6s^{\sqrt{M}}+C_7s^{\sqrt{M}+1}+C_8s^2$$
Where;
$$C_1 =\sqrt{M}-M$$ $$C_2 =(1+\sqrt{M})^2$$ $$C_3 =(1+\sqrt{M})$$ $$C_4 =(2-\sqrt{M})(\sqrt{M}-1)$$ $$C_5=C_6=C_8=(\sqrt{M}-1)^2$$ $$C_7 =-8\sqrt{M}$$