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Solve the differential equation $x^3dy-y\cdot dx=0$

Step-by-step Solution

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Solution

Final answer to the problem

$y=C_1e^{\frac{1}{-2x^{2}}}$
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Step-by-step Solution

How should I solve this problem?

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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

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $-y\cdot dx$ from both sides of the equation

Learn how to solve problems step by step online.

$x^3dy=0- -1y\cdot dx$

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Learn how to solve problems step by step online. Solve the differential equation x^3dy-ydx=0. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -y\cdot dx from both sides of the equation. Multiply -1 times -1. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final answer to the problem

$y=C_1e^{\frac{1}{-2x^{2}}}$

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Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

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Function Plot

Plotting: $x^3dy-y\cdot dx$

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1
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5
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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

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