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Popular >

x^'=(2/t-t)x

Solution

x^{^{'}} = (\frac{2}{t} - t) x

Solution

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

Solution steps

x^{'} (t) = (\frac{2}{t} - t) x

Solve separable ODE:

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

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

Popular Examples

(2x-6}{25}+(2(y-5)(\frac{dy)/(dx)))/9 =1

\frac{2 x - 6}{25} + \frac{2 ( y - 5 ) ( \frac{d y}{d x} )}{9} = 1

(x^2+6x^2y^2)dx+e^{x^3}ydy=0

(x^{2} + 6 x^{2} y^{2}) d x + e^{x^{3}} y d y = 0

y^{9/2}(dy)/(dx)-y^4=-y^{11/2}

y^{\frac{9}{2}} \frac{d y}{d x} - y^{4} = - y^{\frac{11}{2}}

(dx)/(dt)=60-x/(100),x=4000,t=0

\frac{d x}{d t} = 60 - \frac{x}{100}, x = 4000, t = 0

(dy)/(dx)=18+30x+12y+20xy

\frac{d y}{d x} = 18 + 30 x + 12 y + 20 x y

Frequently Asked Questions (FAQ)

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