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Formation of a Differential Equation from a General Solution

The different...

Question

The differential equation by eliminating the arbitary constants from the equation $y = a cos x + b sin x + x sin x$ is

y_{2} + y = 3 cos x

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y_{2} + 2 y = 2 cos x

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y_{2} + y = 2 cos x

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y_{2} + y = 4 cos x

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Solution

The correct option is C $y_{2} + y = 2 cos x$
$y = a c o s x + b s i n x + x s i n x y_{1} = - a s i n x + b c o s x + s i n x + x c o s x ∴ y_{2} = - a c o s x - b s i n x + c o s x + c o s x - x s i n x ∴ y + y_{2} = x s i n x + 2 c o s x - x s i n x = 2 c o s x$

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Similar questions

1

5,

a

b .

\frac{x}{a} + \frac{y}{b} = 1

y^{2} = a (b^{2} - x^{2})

y = a e^{3 x} + b e^{- 2 x}

y = e^{2 x} (a + b x)

y = e^{x} (a cos x + b sin x)

x, y

4 (x^{2} + y^{2}) = a x + b y, 2 (x^{2} - y^{2}) = a x - b y, x y = c^{2}

x \frac{d y}{d x} - y = \sqrt{(x^{2} + y^{2})}

y + \sqrt{(x^{2} + y^{2})} = k x^{2}

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

y =

a cos x + b sin x + x sin x,

y_{1} = \frac{d y}{d x}, y_{2} = \frac{d^{2} y}{d x^{2}}

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