The following statements are all false. For each statement give all reasons why the statement is false. a) e'+3y"=x+ In y is a linear second order ODE. b) y* +2In(x)y'+y'4 xy = sin(x) is a non-linear ODE of order four. c) F(t)-m+y is a non-linear second order ODE. d) y +2y) +3.xy" - cos y is a linear second order ODE.

Q: 1. Determine the equivalent ODE by eliminating arbitrary constants y = ae-2x + bxe-2x Oy" +4y' + y =…

A: Given data:- y=ae-2x+bxe-2x

Q: Let f(x, y, z) = 4xy – z², x = 4r cos(0), y = cos²(0), z = 7r. Use the Chain Rule to calculate the…

A: Given: f(x, y, z)=4xy-z2, x=4r cosθ, y=cos2(θ), z=7r

Q: tan (X) where : Let z=f(x,y) = (10 + 23x)y" where : 13 - e (t – 1) + tan'(t) , and y= (2- t) e'-…

A: Here, the given functions are: z=f(x,y)=(10+23x)ytan xx=13-e2e(t-1)+tan-1(t)y=(2-t)et-13(t-1)

Q: 1. What should be A for the path independent of (2,4) xy + A 2dy – x y? fip- (1,2) Moreover evaluate…

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Q: BCIf the linear ODE N(x,y)y'+M (x,y)%3D0 satisfies the exactness condition, then N (x, y)-S M(x,y)dx…

A: Use the fact that if the second order derivatives of the function f are continuous then the order of…

Q: (1.-13) Show that the line integral (2xy+3)dx +(x² - 4z) dy-4 ydz is independent of path and (0.0,0)…

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Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: 15.4.59 Assume that F(x.y,z(x,y))3D 0 implicitly defines z as a for xyz + 8x + - 4z = 0. dz

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Q: Recall that 1, x >0 d (]xl) dx —1, х<0 x < d Use this result and the chain rule to find (sinx|) for…

A: Here, recall that  -π,-π2 is 3rd quadrant, where sin is -ve-π2,0 is 4th quadrant, where sin is…

Q: 5.) Suppose z = f (x, y) , where x=x(t,r) and y= y(t,r). Assuming all the functions involved have…

A:

Q: An ODE is said to be stable is every arbitrary constant on its solution, such as C1 and C2 for…

A:

Q: The integral of the given function ∫csc^6(x) dx is equal to

A: Need to find ∫cosec6(x) dx

Q: Let f(x, y, z) = 4xy – z² , x = 2r cos(0), y = cos²(0), z = 5r. Use the Chain Rule to calculate the…

A: Given : f(x,y,z)=4xy-z2, x=2rcos(theta) y=cos2(theta) ,z=5r.

Q: Make an example of an autonomous ODE, with stable equilibrium at -1 and 3, and an unstable…

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Q: The function y= is a solution to the 2nd order homogeneous linear ODE t'y" + 4ty' + 2y =0 If you…

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Q: The function y t²y" +4ty' + 2y= 0. If you want, you can verify it! = is a solution to the 2nd order…

A:

Q: 2. Suppose that f(x,y) is a continuous function of two variables such that each of the first and…

A: Consider the given information: Let f(x, y) be the continuous function of two variables such that…

Q: -) A) Find by using chain rule if f = ( , u = -1,x=-1 dx u+1 B) Evaluate the following integral:…

A: This question is based on chain rule differentiation and indefinite integral.

Q: Use the Chain Rule to find az/as and az/at. sin(0) cos(p), 0 = st7, p = s³t əz t³cos(p) cos(0) —…

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Q: 1. Use a Chain rule to find aw and ar aw , if w = x², x = sin(r²s) əs %3D

A: Given w = x2x = sin(r2s)

Q: solve the given nonhomogeneous ODE x^2y"-2xy'+2y=x^3sinx by varition of parametrs

A:

Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Express aw/ar and ôw/as as functions of r ands using chain rule w = = In(x² + y² + z²), x = res sinr…

A: Given problem is :

Q: Let f(x, y, z) = 4xy – z², x = 6r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

A:

Q: Suppose w=x/y+y/z, where x=e3t, y=2+sin(t)x=e3t, and z=2+cos(6t). A ) Use the chain rule to find…

A: w=xy+yz, where x=e3t, y=2+sint &amp; z=2+cos6t Partially differentiating w=xy+yz with respect to x,…

Q: Suppose that w = f(x, y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: By using the chain rule for partial differentiation we will find the value of it.

Q: az and as az Use the chain rule to find at z = In(4x + 3y), x = s sin(t), y = t cos(s) az as az at

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Q: Let f(x, y, z) = 6xy- z, x = 3r cos(0), y = cos (0), z = 3r. Use the Chain Rule to calculate the…

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Q: If f(z,y, z) = I COs(2y – 2). compute and af and Te Əz =I Cos(2y -2). compute O = cos(2y2) I sin(2y…

A: If fx,y,z =xcos2y-z....icompute dfdx and dfdz

Q: Consider the following first-order ODE: d = (1+2x) √9, x = [0, 1], y (x = 0) = 1 Using step size of…

A: consider the following first order ODE dydx=1+2xy with x=0,1 and yx=0=1 claim- use step size h=0.05…

Q: 5. Test the ff ODE for exactness and find the general solution of the DE (2x + 3y) dx + (3x + 4y)…

A: To solve Differential equation.

Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

A:

Q: ди and ди ди Q3. If u = e"" sin p, p= sin x, q = z' In y, r=1/z, use chain rule to find

A: Find your answer below

Q: Show that e, sin x, cos x are linearly independent using Wronskian Method.

A:

Q: If f(x, y, z) = 2 sin(100xy) In(2), compute the value of the limit f(1, h, e) – f(1,0, e) lim h→0 h

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Q: Consider the following ODE system: = x² + xy³ =zy subject to the initial conditions x(0) = 2 and…

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Q: д. L. = a(x, y)+b(x, y) +c(x, y). – d(x, y) -

A: Proof: Consider V be any vector space of all functions of two variable x  and y whose partial…

Q: Assume that all the given functions have continuous second-order partial derivatives. If z = f(x,…

A:

Q: Suppose that w = f(x,y, z), x = h(s), y= g(s, t), z= k(s,t) and all the conditions required for the…

A: Given that w=fx,y,z, x=hs, y=gs,t and z=ks,t. We have to compute ∂w∂t by using chain rule. Since, by…

Q: _Suppose w =+, x = cos² t, y = sin? t, z = ; dw Evaluate at t = 3, by using the Chain Rule dt

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Q: 1. What should be A for the path independent of (2,4) xy + A 2Ay – -dy y? (1,2) Moreover evaluate…

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Q: Let f(x, y, z) = 8xy – z², x = 7r cos(0), y = cos²(0), z = 3r. Use the Chain Rule to calculate the…

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Q: Let w f(t,0) where t and 0 are functions ofr and s, %3D dw is equal to Or then according to the…

A:

Q: Suppose z = x² sin y, x = -s² – 21² , y = 8st. dz A. Use the chain rule to find and * as functions…

A:

Q: Suppose w=x/y+y/z, where x=e^(4t), y=2+sin⁡(4t), and z=2+cos⁡(3t). A ) Use the chain rule to find…

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Q: Show that the functions In x , In(x2) linearly dependent (0, co) are on

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Q: 1-6 Use an appropriate form of the chain rule to find dz/dt. 1. z = 3x²y*; x = r^, y = r² 2. z =…

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Q: Let z = g(x, y) = x² + xy³ -y - 6x - 2y +4, where x = r cos (8) and y = r sin(8). дz Use the chain…

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Q: 16.1. Use an antiderivative to show that for every extending from a point 21 to a point 22 2" dz =…

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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.