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Solve the differential equation $dy=-7x\cdot dx$

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Solution

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Final answer to the problem

$y=-\frac{7}{2}x^2+C_0$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
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1

Integrate both sides of the differential equation, the left side with respect to $y$, and the right side with respect to $x$

Learn how to solve integrals of polynomial functions problems step by step online.

$\int1dy=\int-7xdx$

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Unlock the first 3 steps of this solution

Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy=-7xdx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int1dy and replace the result in the differential equation. Solve the integral \int-7xdx and replace the result in the differential equation.

Final answer to the problem

$y=-\frac{7}{2}x^2+C_0$

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Function Plot

Plotting: $dy+7x\cdot dx$

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Got a different answer? Verify it!

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1
2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Similar Problems Solved

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$\frac{dy}{dx}=\frac{x}{2x-y}$

$\frac{dy}{dx}=\frac{x+3y}{x-y}$

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

See formulas (3)

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