What is the solution for (dy)/(dt)+4y=11,y(0)=1 ?

The solution for (dy)/(dt)+4y=11,y(0)=1 is y=-(7e^{-4t})/4+11/4

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(dy)/(dt)+4y=11,y(0)=1

\frac{d y}{d t} + 4 y = 11, y (0) = 1

y = - \frac{7 e ^{- 4 t}}{4} + \frac{11}{4}

Solution steps

\frac{d y}{d t} + 4 y = 11

Solve separable ODE:

y = - \frac{7 e ^{- 4 t}}{4} + \frac{11}{4}

y = - \frac{7 e ^{- 4 t}}{4} + \frac{11}{4}

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

\frac{x ^{2}}{1 + x ^{3}} d x - \frac{1}{y} d y = 0

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

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

t y^{^{'}} + 2 y = \frac{1}{y ^{2}}

What is the solution for (dy)/(dt)+4y=11,y(0)=1 ?
The solution for (dy)/(dt)+4y=11,y(0)=1 is y=-(7e^{-4t})/4+11/4