y" + 3xy' – 12y = 0, y(0) = 1, y'(0) = 0. y = 9+54x^2+27x^4-27/5x^6 help (formulas)

Q: what is the positive solution to the equation 0 = 1/3 x^2 - 3?

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Q: find y^1 if y= 4^square root of x^2 +1 / x^2 -1

A: To differentiate the given function with respecto to x.

Q: How would I go about sketching z = 4 - 4x^2 - y^2 and z = 2(x^2 - y^2)^(1/2)?

A: Given equation of the curve  z=4-4x2-y2 and z=2x2-y2

Q: How did you integrate (y^2/4)^2

A: We shall solve only the part where there is confusion/doubt as asked in the above question.

Q: solve for y  2xy^2 + 4 = 2(3-x^2y)y', y(-1) = 8

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Q: T(x)= 21 + 25ln (x+1) Find the expression for T^-1 (x)

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Q: If y= 4sqrt(9x^3+10), then y'=

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: Show that for any real constants a and b, where b > 0, (n + a)» = ©(nº)

A: To show for any real constants a and b where b > 0, n+ab=Θnb

Q: Solve using the method of undetermined coefficients: y" + 3y" – 10y' = 2 + xe* %3D

A: Given: y''' + 3y'' - 10y' = 2 + xex

Q: 2 (e^)² = e²x why rather than (e^)² = etz 2

A: To find the integral.

Q: 5x^2−3x−8 has roots at x=

A: Consider the quadratic equation To find - roots

Q: f (x) = 3^x and g(x) = ( 1/3)^x (a) Find f (-1) and g(3) (b) Find f (3/2) and g (-2)

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Q: what is the result of isolating x^(2) in the equation 10x^(2)-36y^(2)=100

A: Algebraic equations 10x^2-36y^2=100

Q: y” + 3y = -48x^2 e^3x

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Q: fill in the boxes with the missing exponets  (5^()x^()y^(-2))/(xy^())=(x^(2)y)/(25)

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Q: y=(x^2+1)^4 y`(1)=?

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Q: Use the product rule to find the derivative of (– 2x" – 4x“) (7e" + 9) Use e^x for e. You do not…

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Q: How does (x-y+3)(x-y+1) = e^2x go to y=(x^2+4x+3-e^2x)/2(x+1) ??

A: Recall  the fact that Now, observe the fact that : ((2)…

Q: why X"/X=-lamba and T"/(a^2)*T=-lamba.

A: Consider the given information: X"/X=T"/(a^2)T =-λ

Q: ∫((3x-4)/((x-1)^2)) dx

A: