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Solve the differential equation $y=\frac{x^{\prime}}{3}$

Step-by-step Solution

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Solution

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Final answer to the problem

$x=\frac{1}{3}\ln\left|y\right|+C_0$
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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

Rewrite the differential equation using Leibniz notation

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

$y=\frac{\frac{dx}{dy}}{3}$

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation y=(x^')/3. Rewrite the differential equation using Leibniz notation. Divide fractions \frac{\frac{dx}{dy}}{3} with Keep, Change, Flip: \frac{a}{b}\div c=\frac{a}{b}\div\frac{c}{1}=\frac{a}{b}\times\frac{1}{c}=\frac{a}{b\cdot c}. Group the terms of the differential equation. Move the terms of the x variable to the left side, and the terms of the y variable to the right side of the equality. Simplify the expression \frac{1}{3}\frac{1}{y}dy.

Final answer to the problem

$x=\frac{1}{3}\ln\left|y\right|+C_0$

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Function Plot

Plotting: $x=\frac{1}{3}\ln\left(y\right)+C_0$

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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

How to improve your answer:

Similar Problems Solved

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$\frac{dy}{dx}=y\left(1-y\right)$

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

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