en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^'=t(1-t)x

Solution

x^{^{'}} = t (1 - t) x

Solution

x = e^{- \frac{t ^{3}}{3} + \frac{t ^{2}}{2} + c_{1}}

Solution steps

x^{'} (t) = t (1 - t) x

Solve separable ODE:

x = e^{- \frac{t ^{3}}{3} + \frac{t ^{2}}{2} + c_{1}}

x = e^{- \frac{t ^{3}}{3} + \frac{t ^{2}}{2} + c_{1}}

Popular Examples

(dy)/(dx)= 1/((xy)^2)

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

y(dy)/(dx)=6x^2

y \frac{d y}{d x} = 6 x^{2}

(dy)/(dx)+18x^2y=5x^2,y(0)=4

\frac{d y}{d x} + 18 x^{2} y = 5 x^{2}, y (0) = 4

(dx)/(dt)+x/(50)=4

\frac{d x}{d t} + \frac{x}{50} = 4

x^5((dy)/(dx))=3x^2sqrt(1-y^2)

x^{5} (\frac{d y}{d x}) = 3 x^{2} 1 - y^{2}

Frequently Asked Questions (FAQ)

What is the solution for x^'=t(1-t)x ?
The solution for x^'=t(1-t)x is x=e^{-(t^3)/3+(t^2)/2+c_{1}}