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Solve the differential equation $\left(t^2+1\right)w^{\prime}+tw=t$

Used Formulas

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Solution

Formulas

Videos

Trigonometric Integrals

$\int\tan\left(\theta \right)dx=-\ln\left(\cos\left(\theta \right)\right)+C$
$\int\sec\left(\theta \right)\tan\left(\theta \right)dx=\sec\left(\theta \right)+C$

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Basic Integrals

· Integral of a Constant
$\int cdx=cvar+C$

Function Plot

Plotting: $w=\frac{\sqrt{t^2+1}+C_0}{\sqrt{t^2+1}}$

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5
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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

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$\frac{dy}{dx}+4y=8$

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

$\frac{dy}{dx}=e^{x-y}+e^x+e^{-y}+1$

$\frac{dy}{dx}=\left(x-y+5\right)^2$

Main Topic: Differential Equations

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

Used Formulas

See formulas (4)

Related Topics

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