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Solve the differential equation $y\frac{dy}{dx}+8x^3=4x$

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Solution

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Final answer to the problem

$y=\sqrt{-\left(1-2x^2\right)^2+C_1},\:y=-\sqrt{-\left(1-2x^2\right)^2+C_1}$
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Step-by-step Solution

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equation
  • Homogeneous Differential Equation
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  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
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1

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $8x^3$ from both sides of the equation

$y\frac{dy}{dx}=4x-8x^3$

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

$y\frac{dy}{dx}=4x-8x^3$

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Learn how to solve differential equations problems step by step online. Solve the differential equation ydy/dx+8x^3=4x. We need to isolate the dependent variable y, we can do that by simultaneously subtracting 8x^3 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 \left(4x-8x^3\right)dx. 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

$y=\sqrt{-\left(1-2x^2\right)^2+C_1},\:y=-\sqrt{-\left(1-2x^2\right)^2+C_1}$

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Function Plot

Plotting: $y\frac{dy}{dx}+8x^3-4x$

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0
a
b
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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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$\frac{dy}{dx}-2y=y^2$

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

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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