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Solve the differential equation $\left(2x+4\right)dx+\left(3y-1\right)dy=0$

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{3}{2}y^2-y=-x^2-4x+C_0$
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Step-by-step Solution

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Grouping the terms of the differential equation

$\left(3y-1\right)dy=-\left(2x+4\right)dx$

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$\left(3y-1\right)dy=-\left(2x+4\right)dx$

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Learn how to solve differential equations problems step by step online. Solve the differential equation (2x+4)dx+(3y-1)dy=0. Grouping the terms of the differential equation. Factor \left(2x+4\right) by the greatest common divisor 2. Integrate both sides of the differential equation, the left side with respect to . Multiply -1 times 2.

Final answer to the problem

$\frac{3}{2}y^2-y=-x^2-4x+C_0$

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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

Linear Differential EquationExact Differential EquationHomogeneous Differential Equation

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Function Plot

Plotting: $\left(2x+4\right)dx+\left(3y-1\right)dy$

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1
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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
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

$\left(1+x^4\right)\cdot dy+x\cdot\left(1+4y^2\right)\cdot dx=0$

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

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

$dx+e^{3x}dy=0$

$factor\left(x^4+x^3-6x^2-4x+8\right)$

$\frac{dy}{dx}=\frac{3x^2+4x+2}{2\left(y+1\right)}$

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

Main Topic: Differential Equations

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

Used Formulas

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