The solid that is the common interior E -V16 - x2 1/2(x² + y?) 14

Q: Using substitution show y = 1+ Ce-t² is a solution to dy + 2ty = 2t dt

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Q: (3) Solue the Initial Value Probles -that SatieSFies the Compleme equation (+) yM -2(x+ Dy! 13 ! %3D…

A: We are given a nonlinear non-homogeneous second order ordinary differential equation, which we have…

Q: Cosider the solid Q x² + 2z = 4 2 If S: x? +2z= 4 Waat the valNe of S 6xZ 4 - x² SP 2² + y? = 4 Y A)…

A: Solution is given below:

Q: (3x y² + 6y? )y' = 2x Find the general solution of the separable DE. %3D

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Q: Solve me initial No need to Jimphiry. by value the separaion of variables a.

A: To solve the following initial value problems by the separation of variables.a y'=1+y2, y0=1b…

Q: e the triple integral: (x+y+z)dydxdz 6 24 18 12

A: Topic :- application of integration

Q: y^2 = 4x, x^2 = 4y; revolving about the x-axis. Use washer method.

A: To find the volume of the solid generated by rotating the region bounded by: about the x-axis.

Q: Use separation of variables to find an explicit solution. xyy' = 2xy² + y² %3D

A: Follow the steps below to solve a differential equation by the variable separation method. First,…

Q: -3 -4 Evaluate: ₂₁ (4x²y - z³) dz dy dx

A: ∫03∫-24∫10(4x2y-z3) dz dy dx

Q: 3. Is y(x) = Cisin2x + C2cos2x, where Ci and C2 are arbitrary constants, a solution of y" + 4y = 0?…

A: Given, y''+4y=0 a second order differential equation. To show that y(x) = C1 sin 2x + C2 cos 2x is a…

Q: / Find the value of the Constant a& b such thet X > 2 fex)=} ax +b iif fer) is Continuny 3 bx - 2, x…

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

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Q: solution is y(t) = c¿e-2t + c2e5t + 4t + cos2t where c,and c2are arbitrary constants. Note: You must…

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Q: 3. Pcx)= 2x²-2x-5 C xo= 1, X,=2 %3D

A: the root of the above equation after 3 iterations is x=1.524   explanation is given below

Q: Q4: Solve by using Separation of variables method? ди =k - for 0 0 at ´əx² u(0,t) = u(L,t) = 0 for…

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Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: 10et --2 Use lap lay trensform system dy, to find the solution of the 1 dx -24, + Y3 +Y2 XP

A: Given system is dy1dx-y2=04y1+dy2dx-4y2-2y3=0-2y1+y2+dy3dx+y3=0 From the first equation of the…

Q: Find a particulaf solutioh to 9y" +6y'-y= 17 A solution is v. (t) =

A: A differential equation is given by, 9y"+6y'-y = 17. The objective is to find the particular…

Q: 2 x 9 = +9 dy %3D

A: As per our guidelines only one question can be solved. The solution is given below for the 1st…

Q: Evaluate the integral. NOTE: Enter the exact answer. xety dy dx

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Q: How do I integrate the following equation? U(z)=2.8*exp(-z/6300)

A: Consider the given equation as Uz=2.8*e-z6300

Q: B. In each exercise, obtain the particular of solution. 2. y(9x - 2y) dx - x(6x – y) dy = 0; when x…

A: Differential equations

Q: pproximate using differentation:  e0.99 Please show step by step solution.

A: This question can be solved using the concept of approximation using derivatives.

Q: Conside the DE y" + a²y = 0; y(T/2a) = 0, y'(1 /2a) = -a where a is a constant. Solve it by using…

A: We are given the DE,                  . where a is constant.  First, we will solve by using trial…

Q: Find the solution. d3x d?x dx – 2–=0 dt + dt3 di2 -21 ® y = c,+c,e'+c,e- -31 D y = c,++ce+c,e-2

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Q: 3. Check for homogeneity and obtain the general solution. (Let 4C=C) (x² + y?)dx + xy dy = 0

A: We will solve the problem

Q: 26. f(y) = y(2 – y), g(y) = %3D

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Q: Q4. Consider the system of equations and detrmine its nature using Jacobi an Analysis. dx = sin(x) –…

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Q: What is the value of x in (2x - 1) + j(x + y) = (y - 6) + j(2y - 4)?   Answer in rectungalur form

A: We have: 2x-1+jx+y=y-6+j2y-4 Comparing both sides: 2x-1=y-6                  ....(1)x+y=2y-4…

Q: Q5. Calculate L-1 -2s e s2 Q6. Find general solution of the DE 4.x?y" + 8xy + y = 0

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Q: What is the antiderivative of q(x) = 2e²+5 – 3sec2 (x – 1)? (Do not include the constant C in your…

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Q: 10 dz where C2 is the top half C2 that is C2: |2| = 2 with z = re", 0 < %3D

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Q: Obtain the general solution unless otherwise instructed . (D² − 3D + 2)y = e²x(1 + e²x) −¹ Yc = Ур =…

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Q: y = e* - Tese x. What is y'= TescX %3D y!? 2. నా

A: Given, y=ex-πcscx We have to find y'.

Q: 2. (6x + y²)dx + y(2x – 3y)dy = 0

A: In this question, we need to check whether the given equation is exact or not and then find the…

Q: Dketch a 3-dhensranal grapn of the equetey 1巻)Z-6-2ーy2 ×Z0 42O 2) 0-

A: 1) given equation to draw the graph is z=16-x2-y2 ,x≥0,y≥0 since x,y are positive the graph will be…

Q: Ans: 2x(x - a)y' = y(3x- 2a) 7. The cubics cy? = x² (x - a) with a held fixed. %3D

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Q: * y"-2xy'+uy = 2, yto)=0, yl)=1 =)ytx)=? %3D find the solution using numerical solution

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Q: y (+zy'+y= ctDsint %3D

A: Given an ordinary non- homogenous differential equation : y(4)+2y'+y=(t+1)sint We need to find the…

Q: find te general Solubton Ror the -y-2² )zX + 2xyzy =2XZ

A: Given: x2-y2-z2zx+2xy.zy=2xz We' will using lagrange's method to solve the given PDE The linear…

Q: Inside the sphere x2 + y2 + z2 = 16 and outside the cylinder x² + y? = 9 %3D

A: The mathematical expression to calculate the volume by double integral. V=∫∫f(x,y)dA=∫∫f(x,y)rdrdθ…

Q: Use separation of variables to find an explicit solution. xyy' = 2xy 2 2 + y?

A: using seperation of variables  and then integrate....

Q: Made in China ry- y+3) %3D Find the generoal solution of the differontial egotion?

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Q: 02 (solve de) * y' = x2 + (1+y²) Arctan x +x²y2 when: x =1, y = 0 %3D %3D %3D Your answer 02…

A: y' = x² + (1+y²) arc tan x + x²y²  So, y' = (1+y²) arc tan x + x² + x²y² So, y' = (1+y²) arc tan x +…

Q: Qi) Solve the following PDES by direct integration. 2) = 0 дх ду 3) = x?y %3D дх ду dxdy azu -2t and…

A: Solve PDE by direct integration.  According to guidelines we solve only first question.

Q: te² i· k) dt V1 – ? 40.

A: Solving by definite integral we have

Q: dy What is the particular solution of x2 y? 2; y= 1 2xy when x dr

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Q: 6 V36 - x2 Vx? + y? dydx : ,2 0 0 (Type an exact answer, using n as needed.)

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Q: 10 Q5/ Evaluate x*dx ,n 5, using trapezoidal rule.

A: The trapezoidal rule formula is: ∫abf(x)dx≈∆x2f(x0+2f(x1)+2fx2+...+2fn-1(x)+f(xn))...(1) where,…

Q: How do you find a cubic function for the quation ?(?)=ax^3+cx^2+d that has a local maximum value of…

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