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Solve the differential equation $xy\cdot y^{\prime}=1+y^2$

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Solution

Formulas

Videos

Learn how solve a system using substitution

https://www.youtube.com/watch?v=oFX16MzHdT4

Solving a system of equations by substitution

https://www.youtube.com/watch?v=xtdy_m_evLI

Solving Trigonometric Equations Using Identities, Multiple Angles, By Factoring, General Solution

https://www.youtube.com/watch?v=VMAMARmmDac

Pre-Calculus - How to solve a trigonometric equation by factoring sec^2(x) -secx=2

https://www.youtube.com/watch?v=JioF8Vm_M60

Simple Differential Equations

https://www.youtube.com/watch?v=C8mudsCSmcU

Example 2: Solving systems by substitution | Systems of equations | 8th grade | Khan Academy

https://www.youtube.com/watch?v=wB3QCk0MGuw

Function Plot

Plotting: $y=\sqrt{C_1x^{2}-1},\:y=-\sqrt{C_1x^{2}-1}$

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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

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Similar Problems Solved

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

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

$\frac{dy}{dx}=y^2-9$

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

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

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

Main Topic: Integration by Trigonometric Substitution

Trigonometric substitution is the substitution of trigonometric functions for other expressions. One may use the trigonometric identities to simplify certain integrals containing radical expressions.

Used Formulas

See formulas (1)

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