Given differential equation y""-ay" -4y' + 8y = e²-³x +8x⁹ (D³ - 20² - Auxilary equation 2 4D +8)y=e +8x9 m²³ - 2m²² 4m +8=0 (m-a) (m+2) m= 2,2, C.F. = Cie Complementary function. 2x = 0 -3x Y₁ = AC వి -3x २x +6x²³x + 3 Let particular integral of D.E. in undetermined Coeff. form -2x 3 + Bx³ + x² + x + E

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A: Domain : It is the set of all real numbers for which the equation is defined.

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A: Solution :limx→7fgx=fg7=f2       g7=2

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A: The given differential equation is;  y''+3y'+2y=1/(8+ex).

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A: See  the details solution in below

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A: Follow the procedure given below.

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A: The given differential equation, d5udr5+7d4udr4-2d3udr3-14d2udr2+dudr+7u=0

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A: Given: f1x=2+x, f2x=x, f3x=x2

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A: We need to find general solution.

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A: As per our norms we have to write one question at a time kindly repost remaining questions.

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Q: Solve the given differential equation by undetermined coefficients. y" - 2y' - 3y = 8ex - 6 y(x) =

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A: Here we have to sketch the graph and then finds its domain and range.

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A: Radius and interval of convergence

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A: Solution ) we have option 3rd  y"+ 4y = 0 Auxilliary equation  m2 + 4 = 0 m2 = -4 m = √( -4 )  m =…

Q: a b = A = B Note: Triangle may not be drawn to scale. Suppose a = 6 and c = 7. Find: B = b O A O

A: Solution: Given:  a=6,    and c = 7 Using Pythagorean theorem

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A: A detailed solution is given below.

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A: On observing curve we will find the interval.

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