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Solve the differential equation $y^{\prime}-y+yx=0$

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Solution

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Final answer to the problem

$\ln\left|y\right|=x-\frac{1}{2}x^2+C_0$
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Step-by-step Solution

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation y^'-yyx=0. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -y+yx from both sides of the equation. Factoring by 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.

Final answer to the problem

$\ln\left|y\right|=x-\frac{1}{2}x^2+C_0$

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Function Plot

Plotting: $\ln\left(y\right)=x-\frac{1}{2}x^2+C_0$

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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 Polynomial Functions

Integrals of polynomial functions.

Used Formulas

See formulas (4)

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