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Joint Entrance Examination
Mathematics
Differential Equations
Question 319
Question 319 of 490
Medium
MCQ
The differential equation representing
y
=
c
1
e
c
2
x
y=c_1e^{c_2x}
y
=
c
1
e
c
2
x
,
c
1
,
c
2
c_1,c_2
c
1
,
c
2
arbitrary, is:
A
y
′
′
=
y
′
y
y''=y'y
y
′′
=
y
′
y
B
y
y
′
′
=
y
′
yy''=y'
y
y
′′
=
y
′
C
y
y
′
′
=
(
y
′
)
2
yy''=(y')^2
y
y
′′
=
(
y
′
)
2
D
y
′
=
y
2
y'=y^2
y
′
=
y
2
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Official solution
y
′
/
y
=
c
2
y'/y=c_2
y
′
/
y
=
c
2
(constant), so differentiating:
y
′
′
y
−
(
y
′
)
2
y
2
=
0
⟹
y
y
′
′
=
(
y
′
)
2
\dfrac{y''y-(y')^2}{y^2}=0 \implies yy''=(y')^2
y
2
y
′′
y
−
(
y
′
)
2
=
0
⟹
y
y
′′
=
(
y
′
)
2
.
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