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Exams
Joint Entrance Examination
Mathematics
Differential Equations
Question 313
Question 313 of 490
Easy
MCQ
The general solution of
d
y
d
x
+
2
x
y
=
x
2
\dfrac{dy}{dx}+\dfrac2xy=x^2
d
x
d
y
+
x
2
y
=
x
2
is:
A
y
=
c
x
−
3
−
x
2
4
y=cx^{-3}-\dfrac{x^2}{4}
y
=
c
x
−
3
−
4
x
2
B
y
=
c
x
3
−
x
2
4
y=cx^3-\dfrac{x^2}{4}
y
=
c
x
3
−
4
x
2
C
y
=
c
x
2
+
x
3
5
y=cx^2+\dfrac{x^3}{5}
y
=
c
x
2
+
5
x
3
D
y
=
c
x
−
2
+
x
3
5
y=cx^{-2}+\dfrac{x^3}{5}
y
=
c
x
−
2
+
5
x
3
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Solutions · 1
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Official solution
I.F.
=
x
2
=x^2
=
x
2
.
y
x
2
=
x
5
5
+
c
⟹
y
=
x
3
5
+
c
x
−
2
yx^2=\dfrac{x^5}{5}+c \implies y=\dfrac{x^3}{5}+cx^{-2}
y
x
2
=
5
x
5
+
c
⟹
y
=
5
x
3
+
c
x
−
2
.
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