en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(xy^')/(e^x+1)=2

Solution

\frac{x y ^{^{'}}}{e ^{x} + 1} = 2

Solution

y = 2 (Ei (x) + ln (x)) + c_{1}

Solution steps

\frac{x y ^{'} ( x )}{e ^{x} + 1} = 2

Isolate

y^{'} (x) : y^{'} (x) = \frac{2 ( e ^{x} + 1 )}{x}

If

f^{^{'}} (x) = g (x)

then

f (x) = \int g (x) d x

y = \int \frac{2 ( e ^{x} + 1 )}{x} d x

\int \frac{2 ( e ^{x} + 1 )}{x} d x = 2 (Ei (x) + ln (x)) + c_{1}

y = 2 (Ei (x) + ln (x)) + c_{1}

Popular Examples

derivative of f(x)=3x^2-24x+45 derivative of

f (x) = 3 x^{2} - 24 x + 45

implicit x^2-6xy+y^2=6 implicit derivative

x^{2} - 6 x y + y^{2} = 6

f (x) = 2 cos (2 x)

laplacetransform 1+5e^{3t}laplace transform

1 + 5 e^{3 t}

derivative of ln(x^5+8ln(x))

\frac{d}{d x} (ln (x^{5}) + 8 ln (x))

Frequently Asked Questions (FAQ)

What is the solution for (xy^')/(e^x+1)=2 ?
The solution for (xy^')/(e^x+1)=2 is y=2(\Ei(x)+ln(x))+c_{1}