What is the solution for (dy)/(dt)=sin(t)-y,y(0)=-1 ?

The solution for (dy)/(dt)=sin(t)-y,y(0)=-1 is y=-(cos(t))/2+(sin(t))/2-1/(2e^t)

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(dy)/(dt)=sin(t)-y,y(0)=-1

\frac{d y}{d t} = sin (t) - y, y (0) = - 1

y = - \frac{cos ( t )}{2} + \frac{sin ( t )}{2} - \frac{1}{2 e ^{t}}

Solution steps

\frac{d y}{d t} = sin (t) - y

Solve linear ODE:

y = - \frac{cos ( t )}{2} + \frac{sin ( t )}{2} - \frac{1}{2 e ^{t}}

y = - \frac{cos ( t )}{2} + \frac{sin ( t )}{2} - \frac{1}{2 e ^{t}}

(x + 1)^{\frac{2}{3}} \frac{d y}{d x} = y^{\frac{1}{3}}

f (x) = \frac{x}{x ^{2} + 49}

\int_{0}^{1} \frac{4}{1 + t ^{2}} d t

ln (1 + x^{2})

x^{2} + 7, 2 x^{2} + 2 x - 1

What is the solution for (dy)/(dt)=sin(t)-y,y(0)=-1 ?
The solution for (dy)/(dt)=sin(t)-y,y(0)=-1 is y=-(cos(t))/2+(sin(t))/2-1/(2e^t)