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Popular >

r^'+2tr=r,r(0)=2

Solution

r^{^{'}} + 2 t r = r, r (0) = 2

Solution

r (t) = 2 e^{t - t^{2}}

Solution steps

r^{'} (t) + 2 t r (t) = r (t)

Solve separable ODE:

r (t) = 2 e^{t - t^{2}}

r (t) = 2 e^{t - t^{2}}

Popular Examples

(dy)/(dx)+x/y =0,y=sqrt(1-x^2)

\frac{d y}{d x} + \frac{x}{y} = 0, y = 1 - x^{2}

(dx)/(dt)=14-42/100 x

\frac{d x}{d t} = 14 - \frac{42}{100} x

y^{^{'}} = k y^{2}

yy^'=(y^2-9)/(x^2+4)

y y^{^{'}} = \frac{y ^{2} - 9}{x ^{2} + 4}

(dy}{dx}=-\frac{2sin(x))/y

\frac{d y}{d x} = - \frac{2 sin ( x )}{y}

Frequently Asked Questions (FAQ)

What is the solution for r^'+2tr=r,r(0)=2 ?
The solution for r^'+2tr=r,r(0)=2 is r(t)=2e^{t-t^2}