Mathematics Daily
Practice
Challenge
Multiplayer
Login
Sign Up
← Question Bank
Question 21
Mu
Differential Equations
★★★★★
Question Bank
⏱ Time: 0:00
Report typo / suggest change
Bookmark
Question
Functions
y
1
,
y
2
,
y
3
y_1,y_2,y_3
y
1
,
y
2
,
y
3
satisfy
y
1
′
+
e
x
ln
(
x
)
y
1
=
0
,
y
1
(
1
)
=
2
,
y_1'+e^x\ln(x)y_1=0,\quad y_1(1)=2,
y
1
′
+
e
x
ln
(
x
)
y
1
=
0
,
y
1
(
1
)
=
2
,
y
2
′
+
e
x
x
y
2
=
0
,
y
2
(
1
)
=
5
,
y_2'+\frac{e^x}{x}y_2=0,\quad y_2(1)=5,
y
2
′
+
x
e
x
y
2
=
0
,
y
2
(
1
)
=
5
,
y
3
′
+
e
x
x
2
y
3
=
0
,
y
3
(
1
)
=
10.
y_3'+\frac{e^x}{x^2}y_3=0,\quad y_3(1)=10.
y
3
′
+
x
2
e
x
y
3
=
0
,
y
3
(
1
)
=
10.
Evaluate
∫
1
e
ln
(
y
1
y
2
2
y
3
)
d
x
\displaystyle\int_1^e\ln\left(\frac{y_1y_2^2}{y_3}\right)\,dx
∫
1
e
ln
(
y
3
y
1
y
2
2
)
d
x
.
A.
(
e
−
1
)
(
ln
5
−
e
)
+
e
e
(e-1)(\ln5-e)+e^e
(
e
−
1
)
(
ln
5
−
e
)
+
e
e
B.
(
e
−
1
)
(
ln
5
+
e
)
−
e
e
(e-1)(\ln5+e)-e^e
(
e
−
1
)
(
ln
5
+
e
)
−
e
e
C.
e
ln
5
−
e
2
+
e
e
e\ln5-e^2+e^e
e
ln
5
−
e
2
+
e
e
D.
e
ln
5
+
e
2
−
e
e
e\ln5+e^2-e^e
e
ln
5
+
e
2
−
e
e
E.
NOTA
Submit
Give Up
← Previous
Next →
Statistics
Attempts: 0
Correct: 0
Best Time: --
Average Time: --