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a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(s)=y_0$ and $y'(s)=y_1$, $s<0$, $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?

a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(s)=y_0>0$ and $y'(s)=y_1$, $s<0$, $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?

a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(0)=y_0$ and $y'(0)=y_1$ $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?

a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(s)=y_0$ and $y'(s)=y_1$, $s<0$, $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?

How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(0)=y_0$ and $y'(0)=y_1$ $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}.$$ Here $n$ is an integer $>2$.

a) How to solve, or at least to prove the existence of a solution to differential equation for given initial condition $y(0)=y_0$ and $y'(0)=y_1$ $$y''+(2-n)\coth(t) y'=\frac{(n-1)\sinh(2y)}{2}, t<0.$$ Here $n$ is an integer $>2$.

b) Can the previous equation have two different solution (with different initial conditions) in $(-2,-1)$, such that one is bounded and the second is not bounded?