In[]:=
DSolve[y'[x]^2==a*y[x]^2+b*y[x]^3+c*y[x]^4,y[x],x]
Out[]=
y[x]
-
a
c
+
a
c
2
Tanh
1
2
-
a
x+
a

1

b
c
a
+2cTanh
1
2
-
a
x+
a

1

,y[x]
-
a
c
+
a
c
2
Tanh
1
2

a
x+
a

1

b
c
a
+2cTanh
1
2

a
x+
a

1

