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

Step-by-step Solution

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Solution

Final Answer

$\frac{1}{4}y-\frac{3}{4}\ln\left(y\right)=\ln\left(x\right)+C_0$
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Step-by-step Solution

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Divide fractions $\frac{1}{\frac{1}{y-3}}$ with Keep, Change, Flip: $a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}$

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

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

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Learn how to solve problems step by step online. Solve the differential equation dy/dx=(4y)/(x(y-3)). Divide fractions \frac{1}{\frac{1}{y-3}} with Keep, Change, Flip: a\div \frac{b}{c}=\frac{a}{1}\div\frac{b}{c}=\frac{a}{1}\times\frac{c}{b}=\frac{a\cdot c}{b}. Multiplying the fraction by y-3. 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

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

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Linear Differential EquationExact Differential EquationSeparable Differential EquationHomogeneous Differential Equation

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Function Plot

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

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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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