# Step-by-step Solution

Go!
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## Step-by-step Solution

Problem to solve:

$\frac{dy}{dx}=x-2y+12$

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

$\frac{dy}{dx}-1\cdot -2y=x+12$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=x-2y+12. Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=2 and Q(x)=x+12. In order to solve the differential equation, the first step is to find the integrating factor \mu(x). To find \mu(x), we first need to calculate \int P(x)dx.

$y=\frac{\frac{1}{2}e^{2x}x+\frac{23}{4}e^{2x}+C_0}{e^{2x}}$
SnapXam A2

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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
Dx
|◻|
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

$\frac{dy}{dx}=x-2y+12$