What is the solution for (dy)/(dx)=2x-y,y(0)=1 ?

The solution for (dy)/(dx)=2x-y,y(0)=1 is y=2(x-1)+3/(e^x)

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

\frac{d y}{d x} = 2 x - y, y (0) = 1

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

Solution steps

\frac{d y}{d x} = 2 x - y

Solve linear ODE:

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

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

x \to 2 lim (x^{2} + 3 x + 5)

\frac{\partial}{\partial x} (e^{- x^{2} - y^{2}})

\int 1 + cos (4 x) d x

\frac{d}{d x} (5 sin (x) - sin (5 x))

\frac{e ^{- 6 s}}{s ^{2} + 2 s - 8}

What is the solution for (dy)/(dx)=2x-y,y(0)=1 ?
The solution for (dy)/(dx)=2x-y,y(0)=1 is y=2(x-1)+3/(e^x)