3- D)y ex+ ex X (В)

Q: 2. Solve the equation 3uy + Uxy 0. (Hint: Let v = u y.) %3D

A: The given problem is to solve the given partial differential equation. Given equation 3uy+uxy=0.

Q: Evaluate using Algebraic Substitution: S In (y + 3) dy o In(vỹ+3) +3vVI - y+ C o (y+ 9) In(vỹ+ 3) +…

A:

Q: 7. - equations. solve the given equations using separable diff 1-4v² dv 6. x- dx ,when x = 3, y = 2…

A: The given differential equation is xdvdx=1-4v23v

Q: uestion 4 1. Nv (~HJA) 2. ~N v H 3. ~H /A To solve the above proof, what rules do you need to use?…

A: we use the logic rules to solve the given problem.

Q: QI: Solve the equation u = 4 uxr 0<x< 5, Ost<00 that satisfies the conditions u(0, t) = 0, u(5, t) =…

A: Given,

Q: proof that: b2 y | VB? - y? dy =Vb² – y? + sin b + c 2

A:

Q: z dz In order to evaluate JA2 – 9 we use the substitution sec e I= 3 sec 0 9. I= -sec 0 4. I= sec 0

A: Indefinite integral by substitution method

Q: The general solution of : y' =y In(y) Select one: a. Inx+ b. C. y=c ex

A: using method of separation

Q: Prove that A → B = (Vx)A B- (Vx)A → (Vy)B, if y is not free in B.

A: To prove that A→B ↦∀x∀A→∀yB, if y is not free in B.

Q: x dy dx x² + y² = In /2 x² X´ + y

A:

Q: 3 y`dy 3 (4 -у?): 2

A:

Q: af Find the values at the point (-7, 3) if and dy 3 S(x, y) = 32x° + 5x²y" + y} – -

A: fx, y=3x5+5x2y3+y23-37 Differentiating wrt x, we get  fxx, y=15x4+10xy3⇒fx-7, 3=15-74+10-733fx-7,…

Q: 100 - x2 - y2 dA where R = {(x, y) I x? + y² s 100,. {(x, v) I x² + y² s 100, x 2

A:

Q: 2. Y, = x is a selution of y-?+ =0. Find the general solution. %3D

A:

Q: dz (D² + 16)*(D² + 4D – 5) (D² + 2D – 3)*z = 0, Dz = dx -

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Q: Any area that is below the x-axis is considered to be --Select-- v and the area above the x-axis is…

A:

Q: 1. Let f(x, y) = Vx³ + y5. Find f2(0,0).

A:

Q: y" + 4y' + 4 = 0, when x = 0, y = 1, y' = -1

A: The given equation is y''+4y'+4=0. The given condition is that,  x=0 ⇒y=1, y'=-1 i.e., y(0)=1;…

Q: Prove this equation by deriving F(x, t) =X(x) Y(y). Please show full steps OF OF 2. +2x- =D0 Ditebak…

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Q: 26. f(y) = y(2 – y), g(y) = %3D

A:

Q: Verify that 2+ ?х ду 2+ дудх : for f(x, y) = 2x³y6 – 4x5y4.

A: Partial differential.

Q: a²z 0²z Determine + Ər² მ02 if z = tan-1 0 r + r r²+02

A:

Q: a inside r= 2 aulside

A: Area is 9.42

Q: the difference between (y, x)

A: The difference between y and x is |y-x|.

Q: secx = -5, <x< TT, then cotx =? Select one: a. cotx =2/6 9. b. cotx= 12 9, c. cotx = 12 d. cotx =…

A: option B is true.

Q: AB =x - 2, AC = 8, BM = 3, CM-= x. x = A

A: In triangle ABC  Given  AM is the bisector of angle BAC AB = x - 2, AC = 8, BM = 3, CM = x

Q: 1. Determine whether the statement is true or false. If it is true, explain why. If it false,…

A:

Q: 8 If x2 = 25 - y2, what is the value of dx2 a²y at the point (3, 4)? 25 (A) - 64 (B) - (C) (D) (E)…

A: use the quotient rule to find the second derivative.

Q: Let then Y F (m,n).

A: Let ,  Now , we want to show that

Q: There is a solution z e C to the equation + 2 = 0. Select one: OTrue OFalse

A:

Q: f (x, y) = 3x2 + y + 4xy + 8 af(z,y) What is the value of when x = 3 and y = 3? dr

A:

Q: Find all a E R that the given equation does not have solution: а — 5 x +1 7+ 3a 2ах — 5 - - - x – 2…

A: Given equation is: a-5x+1-7+3ax-2=2ax-5x2-x-2 Take L.C.M. on left hand side:…

Q: ependent, express your answer in terms of x, where y = y(x).) 0.2x + 0.1y = 0.9 0.3x - 0.3y = 0.6 x,…

A: Given query is to find solution of the system of equations.

Q: n({r E Z| -200 <x < 3 and r is even}) =? %3D Answer: 1 |I

A:

Q: 1- If x? + 2xy = y², then 2 is: dx (e) x+1 (a) y-x x+y (c) (d) —х (b) 2x + 2y ソーズ

A:

Q: 5. (a) Solve the equation + ) = 1. ( Hint: Let v = uz) %3D

A:

Q: If y(#) = and z increases from 0 to 0.5 then dy = 0.5. %3D %3D 1+ *

A:

Q: qunerai solution xy'=y+ Vxy 3. Find the of

A: Given differential equation, xy'=y+xy Find the general solution of the above differential equation…

Q: Solve g(x) = sec (3x2) C.

A:

Q: 35/ SEX √ 2 X-I d x

A:

Q: 10. Jika f(x) = ax · +b, [ f(x)dx =1, dan [S(x)dx = 5, maka nilai a + b = .. (A) - 4 (B) - 3 (C) 3…

A: fx=ax+b,  ∫01fxdx=1  and ∫12fxdx=5

Q: Find possible values of a and b that make the statement true. 2 9. (x) dx + -2 f(x) dx f(x) dx f(x)…

A:

Q: ind V. (V × F), if F(x, y, z) = = V. (V X F) = ezi+ 6xe¹j - 3ek.

A: Topic:- vector algebra

Q: Q.2 Use ODE methods to solve the PDE: U-U₁5, U₁(x,0)=3x², U(0,y)=0 *****

A: Introduction: There are many different approaches that are useful to solve a partial differential…

Q: xy' + y = x?y? 2

A:

Q: A cylindrical pool that has a 3.3 meter radius and is 1.8 meter deep.…

A:

Q: 7) Solve the IVP. 5y" + y' = -6x, y(0) = 0, y'(0) = –10

A:

Q: 9. [y+xy?)dA, R = {(x, y): 0 < x < 2, 1 < ys 2} %3D

A: Definition used -         ∫∫Rf(x,y)dA=∫ab∫cdf(x,y)dydx

Q: Find the general solution of  (D^4+D^2)y=3x^2+4sin(x)-2cos(x) using method of undetermined…

A: The question is solved by using method of undetermined coefficients.

Q: O If Dvaries jointly ® whech of these is The point (2, 3)? Which porntr belongs To the equation? 2x-…

A: 1. D varies jointly with E and F means, D varies directly with respect to E and F or, D is directly…