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Solve (D2-3D+2)y =x(x+4) and show that its general solution is given by y=Aex + Be2x +(x2/2) + (7x/2) + (19/4)

My work :

auxiliary eqn , m2 - 3m + 2= 0 m=1 , m=2

Reduced eqn : yn = Aex + Be2x

P.I. = 1/f(D)F(x) = (1/(D2-3D+2))(x(x+4))

P.I. = [(x2+4x) + ( (1/2)( 2- 3(2x) - 3(4) ) ) + (1/4)(92) )

P.I. = x2 + (4x/2) - (6x/4) - (5/2) + (18/4)

P.I. =(x2/2) + x + 8/4

General solution : y= Aex + Be2x + (x2/2) + x + 8/4

Could anyone point out my mistakes?

Could someone explain how do we verify stokes theorem for the vector field F=zi + (2x+z)j + xk taken over the triangular surface S in the plane (x/1)+(y/2)+(z/3)=1 bounded by the planes x=0 y=0 and z=0. Take boundary of the above triangular surface as the path of the line integral.

For the surface integral I got,

integrate [x=0 - 1] , [y=0 , 2-2x] ( (1/14)*(54 - 38x - 27y) dx dy )

I got the y limit setting z=0 in the plane equation , ==> (y/2) + x = 1==> 2x+y=2 ==> y=2x-2 (Am i correct???)

When working it the other way around using curl, i got Curl F = -i + 2k

N = unt normal vector to the surface =k

N.k = 2/7

(Curl F). N = -2/7

Fnally got the integrate [(-2/7) ÷ (2/7) dx dy] , limits : [x=0 - 1] , [y=0 , 2-2x]

Finally I got -1 as the answer here.

Could someone point out my mistakes please?

Many thanks!

write the required external CSS rules for the following :

Set the font size and font style , of the first bold word of all the paragraphs in a document into 14px and italic respectively.

Derive and draw the world relative supply curve for good 1, which relates the world relative supply of good 1 (q1/q2) to its relative price in world markets (p1/p2). Make sure to label your graph as comprehensively as possible.

Prove that (grad)2 f(r) = D2/dr2 + (2/r) Df/Dr

Where D2/dr2 refers to the second partial derivative of f , w.r.t. r and

Df/ Dr refers to partial derivative of f, w.r.t r

vector r = xi + yj + zk and f(r) is twice differentiable

How do we represent the above facts in 1)axiom form and 2)clausal form

1) All babies are innocent 2) Anyone who is innocent and affectionate will be loved by others 3) Anyone who is loved by others, will receive gifts 4) Teena is an affectionate baby

My thoughts on the question : (Let Vx and Ex denote universal and existential quantifiers respectively )

Let B(x) denote x is a baby I(x) denote x is innocent A(x) denote x is affectionate L(x) denote x is loved by others G(x) denote x receives a gift

Axiom Form : 1) Vx[ B(x) --> I(x) ] 2) Vx[ I(x) ^ A(x) ] --> L(x) 3) Vx [ L(x) --> G(x) ] 4) B(Teena) --> A(Teena)

Have I done the first part correctly? And how do we do the second part?

Thanks!

In the Eduqas GCSE - Paper 2 Writing section - there are 2 questions asking students to write persuasively - eg. in the form of a letter, article, report, review. I can't find a list of what these forms could be - does anyone have any idea if there could be other forms, apart from the ones above? Or if there is a definite list of what might come up? Thank you

Competitive inhibition is when the inhibitor blocks the active site of an enzyme, preventing substrates from binding. Think of this as a defender blocking the goal in a football game to prevent the other team from scoring. Non-Competitive inhibition is when the inhibitor changes the shape of the active sight so the substrate can no longer bind to the enzyme. This would be like a team changing the shape of the net so that the ball no longer fits inside the goal and the other team cant score.

Note ^ means squared

(x+5)2 + (-3) (x+5)2 -3

(x+5)2 - 3 - (10/2)2

(x+5)2 - 3 -25

(x+5)2 -28

The genotype of an organism refers to the genes or alleles in their DNA. The phenotype is the physical expression of this gene and can be observed. The phenotype depends upon the genotype but can also be influenced by environmental factors such as diet.

The genotype of an organism is the genetic code in its cells. This genetic constitution of an individual influences – but is not solely responsible for – many of its traits. The phenotype is the visible or expressed trait, such as hair color. The phenotype depends upon the genotype but can also be influenced by environmental factors.