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Solve the differential equation $2y-2x+\left(2y+2x\right)\frac{dy}{dx}=0$

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Solution

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Final answer to the problem

$yx+\frac{1}{2}y^2=C_0- \left(-\frac{1}{2}\right)x^2$
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Step-by-step Solution

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  • 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
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1

Rewrite the differential equation

Learn how to solve integral calculus problems step by step online.

$\left(2y+2x\right)\frac{dy}{dx}=-\left(2y-2x\right)$

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Unlock the first 3 steps of this solution

Learn how to solve integral calculus problems step by step online. Solve the differential equation 2y-2x(2y+2x)dy/dx=0. Rewrite the differential equation. Group terms with common factors. Rewrite the differential equation. Multiply -1 times 2.

Final answer to the problem

$yx+\frac{1}{2}y^2=C_0- \left(-\frac{1}{2}\right)x^2$

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Function Plot

Plotting: $2y-2x+\left(2y+2x\right)\frac{dy}{dx}$

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Got a different answer? Verify it!

Go!
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
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:

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Main Topic: Integral Calculus

Integration assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

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