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

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$-\ln\left|y\right|+\ln\left|y-1\right|=\ln\left|x\right|+C_0$
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Step-by-step Solution

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Learn how to solve integrals of exponential functions problems step by step online. Solve the differential equation xdy/dx+y=y^2. Multiplying the fraction by x. We need to isolate the dependent variable y, we can do that by simultaneously subtracting y 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}{y^2-y}dy.

Final answer to the problem

$-\ln\left|y\right|+\ln\left|y-1\right|=\ln\left|x\right|+C_0$

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Function Plot

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

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7
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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:

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Main Topic: Integrals of Exponential Functions

Those are integrals that involve exponential functions. Recall that an exponential function is a function of the form f(x)=a^x.

Used Formulas

See formulas (3)

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