1 5earctan(y) dy -1//3 1+ y2 3 1+ у2

Q: Show that there is no solution to the boundary value problem y′′ + 4y = 0, y(0) = 0, y(pai) = 1.

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Q: Solve system of linear DEs  dx/dt+dy/dt+2y+6y=2e^t 2dx/dt+3dy/dt+3x+8y=-1

A: To solve dxdt+dydt+2x+6y=2et2dxdt+3dydt+3x+8y=-1

Q: 6 The non lin ear SYStem 2 2 5 x, - X2 =0 » Xx-Q.25(Sin X, + cCos X2)=0 has solution near

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Q: Cauchy-Euler equations have unique solutions at x=0, specifically the function y = 0.

A: Solution:-

Q: 1) Solve the Boundary Value Problem. y" + y = 0, y(0) = 1, y(z)=1

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Q: 6. Find the general solution of X Ury -Y Uyy = Uy %3D by using the change of variables: v = x, w =…

A: Given: The partial differential equation, xuxy-yuyy=uy   To find: The general solution of the given…

Q: Soru 1 Solve the given initial value problem using the method of Loplace transforms. y "+6 y'+ 5y=12…

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Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: Consider the system dx/dt = 2 dydt = y^2. (a) Calculate the general solution for the system. (b)…

A: Given: Consider the system dx dt=2dydt=y2 To find general solution : dxdt=2⇒x=t+c1 where  c1 is…

Q: у +3у-еX denkleminin genel ҫozйтйпй bulunuz. a. y = e^(-3x)/6 + ce^(-3x) O b. y = e^(3x)/6 +…

A: The given differential equation is                                                      y'+3y=e3x…

Q: d²z 2+ 3-2z = te-2t ; z(0) = 0 z'(0) = -2 dt2

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Q: Question 2 Differentiate y = In(3x – 2x). %3D - 12z3-2 O y'= |3D 3z4-2r 12x – 2 |3D dz 3z4-2z 1 O y'…

A: Explanation of the answer is as follows

Q: 30 -20 -10 Compare dy with (r-y} dydx 10 20 30

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Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

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Q: 7. Show that the system L' = 3y + 2x – r(4x² + 2y²), / = -3r + 2y – y(4.x² + 2y?), has at least one…

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Q: (1 point) Solve the following initial value problem: dy + 7y = 9t dt with y(1) = 9. %3D y =

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Q: If y = y(x) is the solution of the initial-value problem y''+2y'+5y = 0, y(0) = 1, y'(0) = 1, then…

A: To determine the behaviour of the solution at infinity

Q: 2 1. The cissoids y : %D а —х

A: Given the equation  of cissoids y2=x3a-x As per our guideline we are supposed to answer only the…

Q: 2 + 4y = 2e* – 4e¯t, y(0) = 0 dt

A: The given differential equation is,  dydt+4y=2et-4e-t, y(0)=0

Q: 1. Show that y = ze* + e-2* is a solution of y' + 2y = 2e*. 3

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Q: 6. Use Cauchy-Euler equations solution method to solve x³y"' + xy' – y = 0 а.

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Q: 5. Consider the system: dx = x- y+3x-2xy² dt dy =-x+y+3y - 2x'y dt Show that the system has no…

A: Fx+Fy is negative or positive  then the system cannot have no trivial periodic solution

Q: 1. y" - 2y' - 3y = e* by D- operator method

A: Since you have posted multiple questions so according to our guidelines we will solve only first…

Q: •1 cln(5) 1- S SmS) xy evx ´dydx r

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

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Q: Test 1. y" - y - 2y = e by D- operator method 2. y" - 3y' +2y = ex + 6x3 - 2+ 3sin(4x)

A: 1. Now we will solve the differential equation. The genaral solution: =…

Q: (1 point) Use Euler's method with step size 0.1 to estimate y(0.5), where y(x) is the solution of…

A: Here, fx,y=2x+y2h=0.1y0=1 so, x0=0, y0=1

Q: 1. 2xy'+ xy'+ (x² 3) y=O a) Show thet a regulor singulerity Xa>0 is point. 6) Use froteniaw method…

A: (a) Given equation, We know that,

Q: 3 ve the nonhomogeneous system tY' = (²2 =²) x + (-²₁) -21). Y (2-2)

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Q: 2 Discuss the stability of equilibrium points of the following ODE: { (2 = -r³ + y°, y = -x.

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Q: 2. Solve the following Cauchy problem: 1 xYUz + yʻuy y = x2. + yu = y – x with U = -- on

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Q: III 1. dt2 fip +6- dt and the gen +8y=2e-3t am to nor 2. d'y dt2 fip +4 +13y=et dt 3. +10y = e

A: The objective is to find the general solution of the given differential equation.

Q: Show that (0, 0) is an unstable critical point for the following system: 2xy + x3, 1 -x2 + y°. de dy…

A: We will find Jacobian matrix  for system of differential equation Then depend on eigen values of…

Q: %3D у — Зу + Зу - у %3D 4е" y y =

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Q: 2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

A: Answer: The solution is as given below:

Q: The solution to the non-homogeneous DE y' - Бy +ву 3D2х + 3 is 2. a. Ae3x + Be3* +1/3 x + 7/9 b.…

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Q: 1. Use operator / elimination method to solve the given system dx dy + = 2x + 2y + 1 dt dt dx dy y +…

A: Since you posted multiple questions, we will solve first question for you.

Q: 9. Find the solution to satisfying y = dy dt = 7y || y(6)=9

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Q: 28. A trajectory for a system of differential equations with nullcline in below figure conditions x…

A: we have to solve the differential equation.

Q: 2 X u"(x) = −3−2x −²_² +6e² + ½f" (x −1)²u(t)dt, u(0) = 0, u'(0) = 1,u*(0) = 2. - 2

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Q: Let y (z) be the solution of the initial value problem 4) - " + 2y/ + 2y = 0 y (0) =a, y (0)-B, y"…

A: Answer

Q: 1. y" - y' - 2y = e by D- | operator method 2. y" - 3y' +2y = e4x + 6x³ – 2+ 3sin(4x)

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Q: > Reduce the fellouing partial diffrential equation ith constant cobficients into canmonical form…

A: A=4, B=5, C=1, then B2-4AC=25-16=9>0 So, the given pde is the hyperbolic pde. Step 1: We will…

Q: Find the general solution to 3 1 0 0 3 1X. -X= dt 0 2

A: We first find eigen values, then corresponding eigen vector to solve the given system as in next…

Q: 3. yl-2y +2y = ecosx %3D

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Q: solve intial-value problem (x+y)^2dx+(2xy+x^2-2)dy=0      y(1)=1

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Q: y - 3y + 3y – y = 4e* у —

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Q: 1. E(Y,X, X2... X) (Y+Y2 +. + Yn) 2. E(IX,, X2, X) =E Y2+ + Yp) + -B(X, +X +

A: We have to show that β¯ is conditionally distributed.  To show β¯ conditionally distributed we will…

Q: 2nd Case (IBVP Summary) 1.5uxx Ux(0, t) = 0, ux(6 ft, t) = 0, t> 0 (u(x,0) = 80°F, 0 0 1. Obtain…

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