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# Solve the differential equation $y^{\prime}=x+8$

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##  Final answer to the problem

$y=\frac{1}{2}x^2+8x+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• 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
• Integrate using tabular integration
Can't find a method? Tell us so we can add it.
1

Rewrite the differential equation using Leibniz notation

$\frac{dy}{dx}=x+8$

Learn how to solve problems step by step online.

$\frac{dy}{dx}=x+8$

Learn how to solve problems step by step online. Solve the differential equation y^'=x+8. Rewrite the differential equation using Leibniz notation. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(x+8\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

##  Final answer to the problem

$y=\frac{1}{2}x^2+8x+C_0$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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1
2
3
4
5
6
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
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