If n(U) = 80, n(X) = 25,  n(Y) = 35   and n(XUY)' = 20 What is n(X ∩ Y)? Select one: a. 10 b. 0 c. none of the options d. 60

Q: To convert the nonlinear DE xy²y' = y³ – x³ to become a linear DE we use the substitution y= u"…

A: Given the nonlinear DE  xy2y' = y3-x3

Q: |(7) In general, SUT S (SUT)', but (SU T)' S°UT. Pra

A:

Q: .'( , "ג oa3 (125x*y)" 学 A: 125 2 3 $%% 1/3 5メ Y C: D: VONE OF THESE

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: 46. Let the assumed particular solution for the given DE be y, = (Ar³ + Bx² + Cx)e* + E. What is the…

A: A detailed solution is given below.

Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1   Find the general solution.

A: The given differential equation is: y''-y=4cost So, we can also write as: D2-1y=4cost So, the…

Q: Give an e xam Ple of (T, m') ameasurable SPa ce F; x → T {E & CX : fCE) ET3 m is not

A: Given, Τ, m a mesurable space fi:X→Τ , m=E⊆X: f(E)∈Τm is not a σ-algebra on X.

Q: Given that y' = 2x2 – y + 3y2, where y = 0.5 at x = 2. Estimate the values of y(2.2) using the…

A:

Q: ck that y(x) = e rx with r satisfying ar 2

A: Introduction: Introduction: In mathematics, differentiation is the process of determining the…

Q: x*y" + xy'+4y= 2x Ina

A: Cauchy linear differential equation

Q: Let y(x) = c1 + c2x + C3 et is a general solution for D. y" + ay' + by +cy 0, Find the value of a?

A: To answer the given question, we form a differential equation from given general solution.

Q: If a particle is moving with v(x)=1.5(x^1/2) and s(9)=33, what is the position of the particle? As a…

A: Let v(x) denote the velocity of the particle and s(x) denote the position of the particle.Obtain the…

Q: If y = e2t is a solution to y" – 5y' + ay=0 then a=

A:

Q: - If y = e3x and y = e-3x , prove that: - %3D d²y 9y = 0 dx2

A: Given: y=e3x⇒dydx=ddxe3x⇒dydx=3e3xNow,d2ydx2=ddxdydx       =ddx3e3x       =3ddxe3x       =33e3x…

Q: Find the general solution of y' + ny = emx for all m, n. Note: The case m = −n must be treated…

A:

Q: Which of the following is the general solution to (D-3) (D+1) y=0 Oy = (Ao+ At + A2t?) e + Be Oy =…

A: We have to find solutions

Q: 3 3 4) Given xy + xy= 2, Pind y' and y" at the point c4, 4) by implicit di?fexentiation tawi ce,

A: x3y+xy3=2To find→y' and y''   Product rule: ddxu⋅v=u⋅dvdx+v⋅dudx

Q: What is the general solution of zyda - (2 +3y) dy = 0 ? O a + oy In y Cy og In y = C 6y Iny cy? Quiz…

A:

Q: The general solution of the DE: ZV=1 is y=x(x+ c) Select one: O True False

A:

Q: If the solution of the follo wing initial value problem is yo), find yC5) 5xy'-5y= 8X y (1) = 4 %3D…

A:

Q: EXAMPLE 4: WY = In AWXY: WX = 9 m, XY = 15 m, and n ZW =31° m2X = mZY =

A:

Q: 22 To solve y =cy - by' change to u= 1/y?. Substitute for y in um - 2yly³ to find a linear equation…

A:

Q: Q1 but f(x,y) = x²y²sin-'O xf, + yfy = 4f (x,y) between

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Q: Q: Examine y (o.4), Using Runge - Kutta Order 4 method if X = 4n + 2

A: Given y′=4x2+2y,      y(0)=1,   h=0.1,   we have to find y(0.4).Forth order R-K…

Q: 3. Let u(x, t) be the solution to 5ætu, – ut = 0, u(x,0) = 3x², x > 0 - obtained using the method of…

A:

Q: 17. Solve the IVP: y" + 8y(v)? = 1, y(1) = 4, y'(1) = 1/4. Describe the procedure thoroughly and…

A:

Q: 2): Consider the DE y" – y" – 6y = 0 -

A: Follow the procedure given below.

Q: (i) Vx EN By €Z YN Pf W Why? (iv) ar €Z (wsc) vy €N Y N Pf w Why? ax €Z ay ez YN PI W Why?

A:

Q: If integration using u-substitution technique is used to solve for O u = e4x Ou=1-e¹ O U= u = €²x…

A:

Q: 3ey , find Given z = dz dz au

A:

Q: (b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

A:

Q: In AXYZ, PQ I| XY.If XZ= 15, YZ= 12, and ZQ = 8, what is ZP?

A: given XZ=15, YZ=12, and ZQ=8What is ZP?

Q: If f(s) =S+ 25-7, what is Lurite solution in exact form.

A:

Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

A:

Q: (D³ + 2D² − 5D − 8)y = 0, when x = 0, y = 0, y' = 0, y = 2 - -

A: Given  (D3+2D2-5D-8)y=0 and when x=0, y=0, y'=0, y''=2. The formula for differentiation is…

Q: 6. Consider the following model: Yi = Bo+B,D11 + B2D21 +u; O if person i is a non-immigrant) where…

A: Dummy Variable Trap: It is defined as the scenario when the attributes are highly correlted. One…

Q: I For flay 2) = Vxy?z +4x*y, xy,?>0, compute and

A: Both differentiation are solved.

Q: 3. Find the complete solution of the giyen DE using the Method of Variation of Parameters: y" + 44…

A:

Q: 5) *=ClSln t ,y =4 csst t=-2 %3D a) determine dy b) and graeh

A: we have to find derivative

Q: What is the particular solution of (3y2 + 10zy²) dz + (6zy 2+ 10y) dy = 0 when a = 1 and y 2 ? Sry +…

A:

Q: 3. If PY = 3, YZ =5 and PV = 12, find WV. 4. If PW = YZ = 5 and PY = 10, find PV %3D %3D Z. 23

A: Topic:- secant secant method in circles

Q: EX~U(0,1) if Y= =L l(t-x)~ Exporential (A,

A: From the given information, X~U0,1 The probability density function for X is, f(x)=11-0       =1,…

Q: Is a solution of the diffrntish epuation 1 yy'= -X+ with y E € ]_9,GE with x € C-G,G] 2. 3)yy:…

A:

Q: A- If y = e3x and y = e-3x , prove that: - d²y - 9y = 0 - dx2

A:

Q: 2 If [ In(ax)dx = 3, then a = %3D es 4 e4 4 O None e3 4 e6 4

A: Given that: ∫12lnaxdx=3

Q: Q,3 Evaluate [II, xyz dxdydz, 3 < x S-2,0 < y S 1,0 S zs-

A:

Q: 23.Determine the general solution of y′′+λ2y=N∑m=1amsin(mπt),y″+λ2y=∑m=1Namsin(mπt), where λ &gt;…

A:

Q: 3. If V =(3r°y-z,x²+y",-2r:'). Find grad div, at the points (2,-1,0).

A:

Q: If dr/dt= -r5, what is r(t)?

A: Given drdt=-r5. The we have to find r(t) = ?

Q: 2. In AXYZ, PQ || XY . If XZ = 15, YZ = 12, and ZQ = 8, what is ZP? 2.

A: Use concept of similarity. In similar triangle, ratio of corresponding side are equal.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.