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

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{1}{x\left(8\ln\left(x\right)+C_0\right)}$
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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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Rewrite the differential equation in standard form

Learn how to solve differential equations problems step by step online.

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

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Unlock the first 3 steps of this solution

Learn how to solve differential equations problems step by step online. Solve the differential equation xdy/dx+y=-8xy^2. Rewrite the differential equation in standard form. Simplify the fraction \frac{-8xy^2}{x} by x. We identify that the differential equation \frac{dy}{dx}+\frac{y}{x}=-8y^2 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 2.

Final answer to the problem

$y=\frac{1}{x\left(8\ln\left(x\right)+C_0\right)}$

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Function Plot

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

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+
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◻/◻
/
÷
◻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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Similar Problems Solved

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$\frac{dy}{dx}cosx+ysenx=1$

Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

See formulas (2)

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