If ů = (1, 4t, 2t-6)dt, then | |P= 0. V3 9. 3

Q: 4. Solve the equation T _ ²T dt ax satisfying the conditions: (i) T=0 when x= 0 and 1 for all t 2х,…

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Q: 16 – tª -dt t3 Integrate: + C

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Q: 8. Find the orthogonal trajectories of vy = cx

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Q: (ux – u² – x²) dt max subject to х %3D х + и, х(1) 3 2.

A: As per the question we are given a optimization problem, and we will find the optimal control law by…

Q: Calculate the maximum long-term harvest for a population satisfying the DTDS rNt Nt+1 - hNț. 1+ kN{…

A: Given Nt+1=rNt1+kNt-hNt              (1) Given r=1.5 and k=1

Q: Use matrix exponential to find the solution of dx dt 16 5 3 Y, 9. Y, dt x(0) = 1, y(0) = 1

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Q: 8. Find the orthogonal trajectories of Vy = cx

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Q: 3x* – 4y* = C

A: The given equation is: 3x4-4y4=c

Q: Find the value of " dt 2 at the point (0, -1) if xy + y? = 1 5.

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dy + 2t2 - 6y = 0 dt dt? The…

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Q: dr = (t ) dr = (2, -1, 0) SF.dr 2 XYz1-X yJ +z°x K • <2,-1,07 SAXyZ +Xy dt 4 S4(2t)(-t)(1) +…

A: Yes answer is correct...

Q: 4. Solve the equation satisfying the conditions: dt ax (i) T=0 when x= 0 and 1 for all t 2х, 0Sx<1/2…

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Q: Compute. (a) ds/dp if s = 3( p2 + 5p + 1)10 (b) d/dt (at2 + St-1 + S2)

A: (a) We have given s=3p2+5p+110. To find dsdp we have to differentiate s=3p2+5p+110 with respect to…

Q: What guess would would make for the particular solution to the linear, non-homogeneous d'y dy +10 +…

A: Here we will find out the required value.

Q: Which of the following is the orthogonal trajectories of the family of cissoids y² = ? a- y² = C(x +…

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Q: The following linear model dx x(0) = 1000 6x, dt describes growth of populations Select one: True…

A: True.

Q: For the family x² + 3y² = c, find that member of the orthogonal trajectories which passes through…

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Q: 2. Z(t) = v2t – 4 %3D Z'(t) = %3D JOHN GIL AUGUSTO SY JOHN GIL AUGUSTO. C HN GILAU OBYJOHN…

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Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

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Q: x+2 32 dt at x = 4. 2+t 6 Find the linearization of f(x) = 3-

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Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: Obtain the particular solution satisfying the initial conditions indicated. 1. dr / dt = -4rt; when…

A: Given differential equation drdt=-4rt; when t=0,r=r0. The objective is to find the particular…

Q: Find the solution to the boundary value problem: d'y -dy 7- + 10y = 0, y(0) = 9, y(1) = 5 dt dt? The…

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Q: 2: Find the orthogonal trajectories of xy=C.

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Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: (x + 2)-(x + 2)+y 3x +4 diferansiyel denkleminin genel çözümünü dx2 bulunuz. i riiniiz

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Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: Assume Zero initial Conditions * d²y dy +3. + 2y = 0 dt2 dt

A: Solution:

Q: The solution of y" = 8(t – 1) – 6(t – 3), y(0) = y'(0) = 0 is y(t) = %3D (A) (t- 3)[u(t - 1) - u(t-…

A: Given y''=δt-1-δt-3, y0=y'0=0

Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: If Saz dy = In|ly +1- Inly +2| + c, then S- %3D y2+3y+2 dt = e2t +3et+2 In(e' + 1) + In(e + 2) + c…

A: The objective is to find the correct option

Q: 3t – 2 dt t + 1

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Q: 7. a) The error function is defined by 2 er f(æ) = e dt. Show that ť dt = V (erf(b) – er f(a)) 2 and…

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Q: Find constant 3x 1 vectors u and uz such that the solution of the initial value problem 2 -4 -3 x' =…

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Q: Verify that u(z, t) = f(e'r) solves the initial value problem (a,u + z8,u = 0, u(x,0) = f(x).

A: Take the partial derivatives of u(x,t).

Q: What is the equation of the orthogonal trajectories of 4x + 5y = C? (1) 4x + 5y = k (2) 4х — 5у 3Dk…

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Q: Find a general solution to the given Cauchy-Euler equation for t> 0. dy +31- 63y 0 dt dr?

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Q: What is the general solution to the follwoing equation: (4t+5y+4)dt-dy=0

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Q: 6. Solve the second order linear IVP d²y Y at? dy 2 = 1. "6)-1 dt (dt Hint: dt- dy substitute dy…

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Q: Find the solution, including shocks, for solve for t> 0, 0 2.

A: The given P.D.E is                      ut+uux=0,  ................1  ux,0=0,       x&lt;0,2x,…

Q: Solve the following initial value problem for u as a function of t: du/dt+k/ m u = 0 (k and m…

A: Plug du/dt = u' to make it first-order linear equation.

Q: 1 1. S f(x) dt = Choose...

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: d²y +y = d' sec{t) dt dt² dy y(0) = 0; (0) = 1 dt

A: The given differential equation is,d2ydt2-2dydt+y=etsec(t)

Q: 1. SF ·d† = 0 2. ,F ·dT >0 3. ,F ·dT < 0 4. The value of [, F ·dT cannot be determined with only…

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Q: 8. Find the orthogonal trajectories of CX

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Q: Find the general solution of 0= -dy/dt -py-qy^5 by making a suitable substitution that transforms…

A: Given:- 0=-dy/dx-py-qy5 To find:- General solution of given differential equation

Q: X (1) is a WSS process with E [X (t)]=2 and Rxx (7) = 4 + e-0.1 14, Find the mear 1 and variance of…

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Q: do Exercise 0.2.105: Solve ds 8ф аnd ф(0) — -9. %3D Exercise 0.2.106: Solve: d²x dt2 dx a) — 4х,…

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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.