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Solve the differential equation $y^{\prime}=\frac{2x+y}{x+2y}$

Used Formulas

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Solution

Formulas

Videos

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Integrals of Rational Functions

$\int\frac{n}{ax+b}dx=\frac{n}{a}\ln\left(ax+b\right)+C$
$\int\frac{n}{x+b}dx=nsign\left(x\right)\ln\left(x+b\right)+C$

Function Plot

Plotting: $-\frac{1}{4}\ln\left(\frac{y}{x}+1\right)-\frac{3}{4}\ln\left(\frac{-y}{x}+1\right)=\ln\left(x\right)+C_0$

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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:

Similar Problems Solved

$\frac{dy}{dx}=\tan\left(x+y\right)$

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

$\frac{dy}{dx}=\frac{x+3y}{x-y}$

$\frac{dy}{dx}=\frac{x^2+y^2}{2xy}$

$x^2\frac{dy}{dx}-3xy-2y^2=0$

$\frac{dy}{dx}=\frac{4x+3y}{2x+y}$

$\frac{dy}{dx}=\frac{2xy-y^2}{x^2}$

Main Topic: Differential Equations

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

Used Formulas

See formulas (4)

Related Topics

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