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

The solution for (dy)/(dx)= 1/2 x+y-1 is y=-x/2+1/2+c_{1}e^x

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(dy)/(dx)= 1/2 x+y-1

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

y = - \frac{x}{2} + \frac{1}{2} + c_{1} e^{x}

Solution steps

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

Solve linear ODE:

y = - \frac{x}{2} + \frac{1}{2} + c_{1} e^{x}

y = - \frac{x}{2} + \frac{1}{2} + c_{1} e^{x}

y^{^{''''}} + 18 y^{^{''}} + 81 y = 0

x \to 1 lim (x^{2} + 2)

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

\int \frac{ln ( 3 x )}{x} d x

- \frac{18}{t ^{3}} + \frac{3}{t ^{2}}

What is the solution for (dy)/(dx)= 1/2 x+y-1 ?
The solution for (dy)/(dx)= 1/2 x+y-1 is y=-x/2+1/2+c_{1}e^x