Solve first-order DE

V[x_] := 1 - Cos[x];
s1 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] == 5 Pi-1}, u, {x, -20, 20}];
s11 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] ==  Pi+1}, u, {x, -20, 20}];
Plot[{u[x] /. s11,u[x] /. s1}, {x, -20, 20},PlotRange->{0,7 Pi}]
Plot[{1/2 u'[x]^2+ V[u[x]]/. s11,1/2 u'[x]^2+ V[u[x]]/. s1}, {x, -10, 10},PlotRange->{0,5 }]

V[x_]:=1/2 (x^2-1)^2;
Plot[V[x],{x,-2,2}]
s2=NDSolve[{D[u[x],x]==Sqrt[2 V[u[x]]],u[0]==-.1},u,{x,-10,10}];
Plot[u[x]/.s2,{x,-10,10}]

V2[x_]:=1/2 x^2 (x^2-1)^2;
Plot[V2[x],{x,-1.2,1.2}]

s2=NDSolve[{D[u[x],x]==Sqrt[2 V2[u[x]]],u[0]==-.1},u,{x,-10,10}];
Plot[u[x]/.s2,{x,-10,10}]

V[x_]:=1/2 (x^2-1)^2 (x^2-9)^2;
Plot[V[x],{x,-4,4}]
s3=NDSolve[{D[u[x],x]==Sqrt[2 V[u[x]]],u[0]==1.5},u,{x,-10,10}];
s4=NDSolve[{D[u[x],x]==Sqrt[2 V[u[x]]],u[0]==0},u,{x,-10,10}];
Plot[{u[x]/.s3,u[x]/.s4},{x,-1,1},PlotRange->{-1,5}]
Plot[{1/2 u'[x]^2+ V[u[x]]/. s3,1/2 u'[x]^2+ V[u[x]]/. s4}, {x, -1, 1},PlotRange->{0,300 }]