Which of the following is the ODE of the equation Iny = C1e* + 2? Select one: O yy" + y²y' +lny = xe" o Iny = y²y" – y' o y" +y' = y²Iny o y" – y2 – y² Iny = 0

Q: A B с E LL [Choose ] [Choose ] f(x) = 5cos(x) f(x) = cos(x) -4 (x, y+5) f(x)=cos(x)+ 5 (x, 5y) (x,…

A: In this question, the concept of transformation is applied. Transformation A transformation is a…

Q: Evaluate (x²sin y-xcos(y)) dy A x²(1+ sin(1))-xcos (1) + C B x²(1-cos(1))-xsin (1) + C C 2sin…

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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: What is general solution of the given ODE. * dy = cos² (x − y + 1) dx cot (x-y+1) + x + 1 = C Option…

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Q: find the volume of the solid

A: Find volume of solid.Sketch the given function.

Q: Solve the nonlinear 2nd order ODE by reducing it to first order using an appropriate substitution:…

A: The solution is given as

Q: nx and y=cosx from x=- to x=- 4 4

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Q: 4. Find fyryzyaz, if f(r, y) = x² cos[100(e" + /1+ y²)®]

A: Given; f(x,y) = x2cos[100(ey+√(1+y2))y]

Q: Write a first-order non-autonomous ODE with variables t and y that (at least) has the properties…

A: Let us consider a first order non-autonomous ODE with variables y and t as follows dydt=-1ty+t…

Q: S tan5 x dx O 1/4 sec^2 x(sec^2 x - 1) - In Icosx |+ C 1/4 (sec^4 x - sec^2 x -In Icosx |)+ C O 1/4…

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

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Q: Find both first partial derivatives. z = cos(10xy) dz az ду II

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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: 4. y = esec²z (A) sec²rtan resec² z (B)-2 secrtanrx sec²z 5. y= Arccos(x²) 2x (A) √1-2¹ 2x √1-x² (B)…

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Q: 19. Evaluate: S A. VT- x² + arcsin x + C C. – VT- x² + 3arc cos x + C B. – VI- x2 +3 arcsin x + C D.…

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Q: ze : use the Implicit Differentition to find ax 'ay 1) 3yz2 - e4* cos 4z - 3y2 = 4

A: 3yz2-e4xcos4z-3y2=4

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

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Q: 8. lim,0 1-cos x 2x2 1 (a) 1 (b) – (c) 0 (d) ; (e) 1. -

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Q: Find both first partial derivatives. z = cos(5xy) az ax az ду II II

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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…

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Q: Differentiate y=excos(x2): y'= A. excos(x2)-2xsin(x2) B. -2xexsin(x2) C. ex(cos(x2)-2xsin(x2))…

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Q: Evaluate. d farctan a – In a] dæ 1+x² 1 sec2 x 1 :- e" sec² ¤ 1 + 1-x²

A: The rule of derivatives states that ddx(f(x)±g(x))=ddx(f(x))±ddx(g(x))

Q: Find the right match for the following ODEs in the dropdown menu y' = y" JS sin(x) 5xy' = y - 3x²y"…

A: This is a problem related to differential equation. Please find the answer as below.

Q: Solve each of the foiiowing ODES 1. (3x?y + 4x°)dx + (x³-ycosy-siny)dy = 0 2. (4x³y3 + 6xy²)dx +…

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Q: дz If x² sin(2y - 5z) = 1 + y cos(6zx) defines z implicitly as a function of x and y, find [Show…

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Q: Find the right match for the following ODES in the dropdown menu y = y" sin(x) + e* + 2 Choose... 令…

A: Please see the below picture for detailed solution.

Q: b) Show that the ode (x + tan-¹ y) dx + x+y dy = 0 is exact, then find the general solution and 1+y²…

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Q: 5(t - )cos3t) 3 252 + 18

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Q: Find dy if y= 5x² sin4x dr O None -20x? cos4x – 10xsin4x 20x² cos4x + 10xsin4x O 10x² cos4x +…

A: We apply u*v rule of derivatives d/dx (u*v) = v*du/dx + u *dv/dx

Q: when y=cos0 is horizontally factored by a factor of 1/4. y=co s1/4 θ y=cos θ + 1/4 y=1/4 cos θ…

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Q: Calculate the first, second, and third derivatives of y(t) = 2016/5 – 6127. (Use symbolic notation…

A: We will use simple differentiation rules to solve this question.

Q: Consider the ODE 4 = -y3 + 3y² + 10y. i) Explain why this is an autonomous ODE ii) Determine all the…

A: In this question, we an autonomous differential equation. For the given differential equation we…

Q: 1. Evaluate f sin*(2x + 3)cos (2x + 3) dx sin(2x + 3) put = t 2. Evaluate f dx Put x2 + 5 = t x2+5…

A: Explanation of the solution is given below.....

Q: 9. Evaluate y' of y = e-2*sin3x a. 3e-cos3x- 2y b. 3e-cos3x- 3y c. 3ecos3x - y d. 3e-cos3x +y e. Not…

A: Explanation of the answer is as follows

Q: Specify c_1, Co, C1 and p such that the formula y'(t) 2 k¯P(c_1y(t – k) + coy(t) + ciy(t + k))…

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Q: az Use an appropriate form of the chain rule to find dt 1 z = 2 cos x sin xy; y = 5t t Enter the…

A: z=2 cos x-sin xy ; x=1t; y=5t   see z is a function of x and y ,where x and y are functions of t so…

Q: Solve the given nonhomogeneous linear ODE by variation of parameters or undetermined coefficients.…

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Q: Solve the following ODE y' + tan(2 - x)y = 0 with initial condition y(0) = 3

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Q: 3. Given that 2 = 6²¹ sin (u + ), e2v Use chain rule to find az/0x when x = 0, y = 0. u=e¹ - sin (y…

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Q: Find L{(t- 2) (3 cos 5t + 1)}. COS 3(s2-25) (s²+25)? 30 | s2 s2 +25 6. 3 g3 s2 s2 +25 s(s² +25) 6s…

A: Find the Laplace transform of  L{(t-2)(3cos5t+1)}

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: 1. If y = cos(2t + 5) find using chain rule dt

A: Giveny=cos(2t+5)

Q: .2 Suppose that w = x² + y² – z2 And x = psin(4)cos(0), y = psin(4)sin(0), z = pcos(4) Use…

A: The Solution is given in next steps

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

A: fx,y,z=6xy-z2x=3r cosθy=cos2θz=3r

Q: Q# (17' Compute: [tan (10x)sec(10x)dx tan³ 1 tan(10x)+C 10 1 A) tan (10x) – 3 30 1 1 В) sec (10x)--…

A: We use substitution method to solve the Integral.

Q: 3 – 2ry' + 2y = x° sin x

A: The general solution will be the sum of the complementary solution and particular solution.   The…

Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

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Q: 3: Solve ODE Cist Order a. dY

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Q: Suppose f (x) =cos( 2– 3x). Evaluate: )dx A - 3sin(3x – 2) +C ® -;sin(3x – 2) + C sin(3x – 2) + C D…

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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.