What is the solution for (dy)/(dx)=-0.5y+x ?

The solution for (dy)/(dx)=-0.5y+x is y=2x-4+(c_{1})/(e^{0.5x)}

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(dy)/(dx)=-0.5y+x

\frac{d y}{d x} = - 0.5 y + x

y = 2 x - 4 + \frac{c _{1}}{e ^{0.5 x}}

Solution steps

\frac{d y}{d x} = - 0.5 y + x

Solve linear ODE:

y = 2 x - 4 + \frac{c _{1}}{e ^{0.5 x}}

y = 2 x - 4 + \frac{c _{1}}{e ^{0.5 x}}

\int \frac{x}{3} d x

y^{^{''}} + 3 y = - 9

- 2 cot (x) csc (x)

x \to 2 π lim (\frac{1}{sin ( x )})

sin (2 x)

What is the solution for (dy)/(dx)=-0.5y+x ?
The solution for (dy)/(dx)=-0.5y+x is y=2x-4+(c_{1})/(e^{0.5x)}