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# Solve the differential equation $5\left(\frac{dy}{dx}\right)+4xy=10$

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##  Final answer to the problem

$e^{\frac{2}{5}x^2}y=2\sum_{n=0}^{\infty } \frac{\left(\frac{2}{5}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• 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
Can't find a method? Tell us so we can add it.
1

Divide all the terms of the differential equation by $5$

$\frac{5}{5}\frac{dy}{dx}+\frac{4xy}{5}=\frac{10}{5}$

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

$\frac{5}{5}\frac{dy}{dx}+\frac{4xy}{5}=\frac{10}{5}$

Learn how to solve differential equations problems step by step online. Solve the differential equation 5dy/dx+4xy=10. Divide all the terms of the differential equation by 5. 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)=\frac{4x}{5} and Q(x)=2. 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.

##  Final answer to the problem

$e^{\frac{2}{5}x^2}y=2\sum_{n=0}^{\infty } \frac{\left(\frac{2}{5}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$

##  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

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0
a
b
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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

###  Main Topic: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.