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Solve the differential equation $x\frac{dy}{dx}+9y=8y^2$

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Solution

Final answer to the problem

$y=\frac{-9}{C_1x^{9}-8}$
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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 $9y$ from both sides of the equation

$x\frac{dy}{dx}=8y^2-9y$

Learn how to solve problems step by step online.

$x\frac{dy}{dx}=8y^2-9y$

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Learn how to solve problems step by step online. Solve the differential equation xdy/dx+9y=8y^2. We need to isolate the dependent variable y, we can do that by simultaneously subtracting 9y from both sides of the equation. 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}{8y^2-9y}dy. 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

$y=\frac{-9}{C_1x^{9}-8}$

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Function Plot

Plotting: $x\frac{dy}{dx}+9y-8y^2$

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1
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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

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