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Solve the differential equation $e^xdy=2x\cdot dx$

Step-by-step Solution

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Solution

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Final answer to the problem

$y=\frac{-2x-2}{e^x}+C_0$
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Step-by-step Solution

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Learn how to solve integration by parts problems step by step online. Solve the differential equation e^xdy=2xdx. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Taking the constant (2) out of the integral. Solve the integral \int1dy and replace the result in the differential equation.

Final answer to the problem

$y=\frac{-2x-2}{e^x}+C_0$

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Function Plot

Plotting: $e^xdy-2x\cdot dx$

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0
a
b
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d
f
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m
n
u
v
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x
y
z
.
(◻)
+
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×
◻/◻
/
÷
◻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

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

$ydy=4x\left(y^2+1\right)^{\frac{1}{2}}dx$

$\frac{dy}{dx}=\sin5x$

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

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

$\frac{dy}{dx}=y^2-4$

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

Main Topic: Integration by Parts

Integration by parts is an integration method that relates the integral of a product of two or more functions to the integral of their derivative and antiderivative.

Used Formulas

See formulas (5)

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