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Solve the differential equation $\frac{dy}{dx}=2\left(1+x\right)\left(1+y^2\right)$

Step-by-step Solution

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Solution

Final answer to the problem

$y=\tan\left(2x+x^2+C_0\right)$
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Step-by-step Solution

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Learn how to solve problems step by step online. Solve the differential equation dy/dx=2(1+x)(1+y^2). Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression 2\left(1+x\right)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(2+2x\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.

Final answer to the problem

$y=\tan\left(2x+x^2+C_0\right)$

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Function Plot

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

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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

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