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Solve the differential equation $\frac{dz}{dt}+e^{\left(t+z\right)}=0$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$z=\ln\left(\frac{-1}{-e^t+C_0}\right)$
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Step-by-step Solution

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Learn how to solve integral calculus problems step by step online. Solve the differential equation dz/dt+e^(t+z)=0. Grouping the terms of the differential equation. x+0=x, where x is any expression. Apply the property of the product of two powers of the same base in reverse: a^{m+n}=a^m\cdot a^n. Group the terms of the differential equation. Move the terms of the z variable to the left side, and the terms of the t variable to the right side of the equality.

Final answer to the problem

$z=\ln\left(\frac{-1}{-e^t+C_0}\right)$

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Function Plot

Plotting: $\frac{dz}{dt}+e^{\left(t+z\right)}$

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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:

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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.

Used Formulas

See formulas (4)

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