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Popular >

(dx)/(dt)=t+2tx

Solution

\frac{d x}{d t} = t + 2 t x

Solution

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

Solution steps

\frac{d x}{d t} = t + 2 t x

Solve separable ODE:

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

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

Popular Examples

y^'=(1-x^2)/(y^2)

y^{^{'}} = \frac{1 - x ^{2}}{y ^{2}}

y^{^{'}} + 3 y^{^{'}} + 2 y = 0

(2 x - 1) y^{^{'}} + 2 y = 0

(dy}{dt}=4t(sin(y))^2,y(-1)=\frac{5pi)/4

\frac{d y}{d t} = 4 t (sin (y))^{2}, y (- 1) = \frac{5 π}{4}

y=(x^2(2+x))/((1+x)^2)y^'

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

Frequently Asked Questions (FAQ)

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