Solve the differential equation $\frac{1}{\sqrt{1-x^2}}dx+\frac{1}{\sqrt{1-y^2}}dy=0$

Step-by-step Solution

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Final answer to the problem

$y=\sin\left(-\arcsin\left(x\right)+C_0\right)$
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Step-by-step Solution

How should I solve this problem?

  • Separable Differential Equation
  • Exact Differential Equation
  • Linear Differential Equation
  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
  • Integrate by substitution
  • Integrate by parts
  • Integrate using tabular integration
  • Load more...
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Grouping the terms of the differential equation

$\frac{1}{\sqrt{1-y^2}}dy=-\left(\frac{1}{\sqrt{1-x^2}}\right)dx$

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$\frac{1}{\sqrt{1-y^2}}dy=-\left(\frac{1}{\sqrt{1-x^2}}\right)dx$

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Learn how to solve problems step by step online. Solve the differential equation 1/((1-x^2)^(1/2))dx+1/((1-y^2)^(1/2))dy=0. Grouping the terms of the differential equation. Multiplying the fraction by -1. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{\sqrt{1-y^2}}dy and replace the result in the differential equation.

Final answer to the problem

$y=\sin\left(-\arcsin\left(x\right)+C_0\right)$

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Function Plot

Plotting: $\frac{1}{\sqrt{1-x^2}}dx+\frac{1}{\sqrt{1-y^2}}dy$

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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
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

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