What is the solution for (1+y)(dy)/(dt)=6t,\quad y(2)=5 ?

The solution for (1+y)(dy)/(dt)=6t,\quad y(2)=5 is y=(-2+sqrt(24t^2+48))/2

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(1+y)(dy)/(dt)=6t,\quad y(2)=5

(1 + y) \frac{d y}{d t} = 6 t, y (2) = 5

y = \frac{- 2 + 24 t ^{2} + 48}{2}

Solution steps

(1 + y) \frac{d y}{d t} = 6 t

Solve separable ODE:

y = \frac{- 2 + 24 t ^{2} + 48}{2}

y = \frac{- 2 + 24 t ^{2} + 48}{2}

\int \frac{x ^{2} - 2}{x + 3} d x

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

\frac{d}{d x} (\frac{( x - 3 ) ( 3 x - 25 )}{x})

f (x) = x^{2} + 5 x - 2, at x = - 1

x \to 0 + lim (\frac{6}{x ^{2} - x})

What is the solution for (1+y)(dy)/(dt)=6t,\quad y(2)=5 ?
The solution for (1+y)(dy)/(dt)=6t,\quad y(2)=5 is y=(-2+sqrt(24t^2+48))/2