In[]:=
sol=DSolve[{X''[x]+λ^2X[x]==0,X[0]==0,X[1]==0},X,x]
Out[]=
XFunction{x},

1
Sinx
2
λ

n.∈&&n.≥1&&
2
λ

2
n.
2
π
0
True

In[]:=
m=sol[[1]]
Out[]=
XFunction{x},

1
Sinx
2
λ

n.∈&&n.≥1&&
2
λ

2
n.
2
π
0
True

In[]:=
X[x]/.m
Out[]=

1
Sinx
2
λ

n.∈&&n.≥1&&
2
λ

2
n.
2
π
0
True
In[]:=
Plot[Evaluate[X[x]/.sol/.{

1
->1,n->2}],{x,-1,1}]
Out[]=
-1.0
-0.5
0.5
1.0
-1.0
-0.5
0.5
1.0