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Solve the differential equation $\frac{dy}{dx}=\frac{4y}{x\left(y-3\right)}$

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Solution

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Final answer to the problem

$\frac{1}{4}y-\frac{3}{4}\ln\left|y\right|=\ln\left|x\right|+C_0$
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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

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

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

$\frac{1}{4y}\left(y-3\right)dy=\frac{1}{x}dx$

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation dy/dx=(4y)/(x(y-3)). 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. Simplify the expression \frac{1}{4y}\left(y-3\right)dy. 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 \int\frac{y-3}{4y}dy and replace the result in the differential equation.

Final answer to the problem

$\frac{1}{4}y-\frac{3}{4}\ln\left|y\right|=\ln\left|x\right|+C_0$

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Function Plot

Plotting: $\frac{dy}{dx}+\frac{-4y}{x\left(y-3\right)}$

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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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$\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)$

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

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

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

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