en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(dx)/(dt)+x=-e^t

Solution

\frac{d x}{d t} + x = - e^{t}

Solution

x = - \frac{e ^{t}}{2} + \frac{c _{1}}{e ^{t}}

Solution steps

\frac{d x}{d t} + x = - e^{t}

Solve linear ODE:

x = - \frac{e ^{t}}{2} + \frac{c _{1}}{e ^{t}}

x = - \frac{e ^{t}}{2} + \frac{c _{1}}{e ^{t}}

Popular Examples

derivative of (3t^2-t+a^2^{101})

\frac{d}{d x} ((3 t^{2} - t + a^{2})^{101})

limit as x approaches+3+of 7/(x-3)

x \to + 3 + lim (\frac{7}{x - 3})

(\partial)/(\partial x)(-2y)

\frac{\partial}{\partial x} (- 2 y)

integral of (sqrt(a^2+x^2))/(x^4)

\int \frac{a ^{2} + x ^{2}}{x ^{4}} d x

integral of (7x^2)/((x+1)(x^2+1))

\int \frac{7 x ^{2}}{( x + 1 ) ( x ^{2} + 1 )} d x

Frequently Asked Questions (FAQ)

What is the solution for (dx)/(dt)+x=-e^t ?
The solution for (dx)/(dt)+x=-e^t is x=-(e^t)/2+(c_{1})/(e^t)