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Differential Equations
Related Topics
Wize University Linear Algebra Textbook > Differential Equations
Basics of Differential Equations
6 Activities
Solve the differential equation
d
y
d
x
=
4
y
x
\frac{dy}{dx}=\frac{4y}{x}
d
x
d
y
=
x
4
y
,
x
>
0.
x>0.
x
>
0.
y
=
\ds\bcb{y=}
y
=
I don't know
Check Submission
More Basics of Differential Equations Questions:
Practice: Linear DE
Q
:
\bf{Q:}
Q
:
Solve
x
2
d
y
d
x
+
3
x
y
=
1
x^2 \dfrac{\de{y}}{\de{x}} + 3xy = 1
x
2
d
x
d
y
+
3
x
y
=
1
Find a solution to the differential equation
d
y
d
t
=
3
y
\frac{dy}{dt}=3y
d
t
d
y
=
3
y
where
y
(
0
)
=
6
y(0) = 6
y
(
0
)
=
6
.
Solve the differential equation
d
y
d
x
+
(
tan
x
)
y
=
sin
x
\frac{dy}{dx}+\left(\tan\ x\right)y\ =\sin x\
d
x
d
y
+
(
tan
x
)
y
=
sin
x
subject to
y
(
2
π
)
=
π
3
.
y\left(2\pi\right)=\frac{\pi}{3}.
y
(
2
π
)
=
3
π
.
Differential Equations
The functions
y
=
x
2
+
c
x
2
y=x^2+\frac{c}{x^2}
y
=
x
2
+
x
2
c
, are all solutions of equation:
x
y
′
+
2
y
=
4
x
2
,
x
>
0.
xy'+2y=4x^2,\ x>0.
x
y
′
+
2
y
=
4
x
2
,
x
>
0.
Find the constant
c
c
c
which produces a solution which also satisfies the initial condition
y
(
6
)
=
5.
y\left(6\right)=5.
y
(
6
)
=
5.
Differential Equations
Find an equation of the curve that satisfies
d
y
d
x
=
80
y
x
15
\frac{dy}{dx}=80yx^{15}
d
x
d
y
=
80
y
x
15
and whose y-intercept is
6
6
6
.
Differential Equations
Let
y
′
=
7
x
y'=7x
y
′
=
7
x
. Find all values of
r
r
r
such that
y
=
r
x
2
y=rx^2
y
=
r
x
2
satisfies the differential equation.
List all the values separated by a comma.