+
1
15.
Form the differential equation which has
complete integral.
e2y + 2 a xe + d= 0 for its
2
x + x + c
where
Answers
Answer:
Can you please give a correct question!!!!
Please!
I can't understand this que!!!
dy
+2y=lnx
dx
dy
+
x
2y
=
x
lnx
It is first order linear differential equation
P=
x
2
,Q=
x
lnx
I.F.=e
∫P.dx
=e
∫
x
2
dx
=e
2lnx
=x
2
solution of D.E. is
y×I.F.=∫Q×I.F.dx+C
y×x
2
=∫
x
lnx
×x
2
dx+C
Putting lnx==t,x=e
t
,
x
1
dx=dt
yx
2
=∫t.e
2t
dt+C
Integration by parts taking t as first function
x
2
y=t
2
e
2t
−∫1.
2
e
2t
dt+C
x
2
y=
2
te
2t
−
4
e
2t
+C
x
2
y=
2
lnx×x
2
−
4
x
2
+C
Putting x=e, we get
e
2
y(e)=
2
e
2
−
4
e
2
+C ---- (i)
Putting x=1, we get
y(1)=−
4
1
+C ----- (ii)
Subtracting (i) from (ii)
e
2
y(e)−y(1)=
4
e
2
+1
Answer By
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