What is the answer to x^2y+xy-k^2y=0 ?

The answer to x^2y+xy-k^2y=0 is y=0,x=(-1+sqrt(1+4k^2))/2 ,x=(-1-sqrt(1+4k^2))/2

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x^2y+xy-k^2y=0

x^{2} y + x y - k^{2} y = 0

y = 0, x = \frac{- 1 + 1 + 4 k ^{2}}{2}, x = \frac{- 1 - 1 + 4 k ^{2}}{2}

Solution steps

x^{2} y + x y - k^{2} y = 0

Factor out common term

y

y (x^{2} + x - k^{2}) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

y = 0 or x^{2} + x - k^{2} = 0

y = 0

Solve

x^{2} + x - k^{2} = 0 : x = \frac{- 1 + 1 + 4 k ^{2}}{2}, x = \frac{- 1 - 1 + 4 k ^{2}}{2}

The solutions are

y = 0, x = \frac{- 1 + 1 + 4 k ^{2}}{2}, x = \frac{- 1 - 1 + 4 k ^{2}}{2}

t e^{t} (c - 2 x) = 0

∣ a ∣ b = 0

- 2 x e^{y} = 0

c a = 0

(x^{2} D^{2} + 2 x D - 2) y = 0

What is the answer to x^2y+xy-k^2y=0 ?
The answer to x^2y+xy-k^2y=0 is y=0,x=(-1+sqrt(1+4k^2))/2 ,x=(-1-sqrt(1+4k^2))/2