What is the answer to D(x)=50-0.25x ?

The answer to D(x)=50-0.25x is x=(200)/(4D+1);\quad D\ne-1/4

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D(x)=50-0.25x

D (x) = 50 - 0.25 x

x = \frac{200}{4 D + 1}; D \neq = - \frac{1}{4}

Solution steps

D (x) = 50 - 0.25 x

Multiply both sides by

100

D x \cdot 100 = 5000 - 25 x

Move

25 x

to the left side

D x \cdot 100 + 25 x = 5000

Factor

D x \cdot 100 + 25 x : 25 x (4 D + 1)

25 x (4 D + 1) = 5000

Divide both sides by

25 (4 D + 1); D \neq = - \frac{1}{4}

x = \frac{200}{4 D + 1}; D \neq = - \frac{1}{4}

y^{^{''}} + 2 y^{^{'}} + 5 y = 5

y^{^{''}} + 9 y = cos (9 x)

y^{^{''}} - y^{^{'}} - 6 y = 32 cos (3 x)

y^{^{'''}} - 3 y^{^{'}} + 2 y = e^{- 2 x}

y^{^{''}} - 2 y^{^{'}} + 2 y = e^{- t}, y (0) = 0, y^{^{'}} (0) = 3

What is the answer to D(x)=50-0.25x ?
The answer to D(x)=50-0.25x is x=(200)/(4D+1);\quad D\ne-1/4