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

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{C_1e^{\frac{1}{-x}}}{x}$
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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

Factor the polynomial $y-yx$ by it's greatest common factor (GCF): $y$

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

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

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation (x^2dy)/dx=y-yx. Factor the polynomial y-yx by it's greatest common factor (GCF): y. 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}{x^2}\left(1-x\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

$y=\frac{C_1e^{\frac{1}{-x}}}{x}$

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Function Plot

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

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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

How to improve your answer:

Similar Problems Solved

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

$\frac{dy}{dx}=y^2-4$

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

$\frac{dy}{dx}=y\left(y+2\right)$

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

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

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

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

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