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Solve the differential equation $5\left(\frac{dy}{dx}\right)+4xy=3$

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Solution

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Final answer to the problem

$e^{\frac{2}{5}x^2}y=\frac{3}{5}\sum_{n=0}^{\infty } \frac{\left(\frac{2}{5}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$
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Step-by-step Solution

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1

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

Learn how to solve integrals of polynomial functions problems step by step online.

$\frac{5}{5}\frac{dy}{dx}+\frac{4xy}{5}=\frac{3}{5}$

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Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation 5dy/dx+4xy=3. 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)=\frac{3}{5}. 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

$e^{\frac{2}{5}x^2}y=\frac{3}{5}\sum_{n=0}^{\infty } \frac{\left(\frac{2}{5}\right)^nx^{\left(2n+1\right)}}{\left(2n+1\right)\left(n!\right)}+C_0$

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Function Plot

Plotting: $5\left(\frac{dy}{dx}\right)+4xy-3$

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0
a
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n
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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:

Similar Problems Solved

$\frac{dy}{dx}=xy+1$

$\frac{dy}{dx}=xy-1$

$y'-xy=1-x$

$\frac{dy}{dx}=1+xy$

$\frac{dy}{dx}=2xy+1$

$\frac{dy}{dx}-2xy=2$

$\frac{dy}{dx}=xy+3$

Main Topic: Integrals of Polynomial Functions

Integrals of polynomial functions.

Used Formulas

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