- Example 3.3 Verify that on the interval (-, ), X1(t) = () and X2() = (-») are %3D solution of dxi = x1 - 4x2 dt dx2 2x1 - 5x2 dt

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A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

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A: Recall the order of a differential equation of a given relation is the number of arbitrary constants…

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A: x = 0 r cos θ = 0 θ = π2 x = 322 r cos θ = 322 r = 322 sec θ   y = x r sin θ = r cos θ θ =…

Q: 16. Sinusoidal functions do not have any critical points.

A: False. Sinusoidal functions has critical points.

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Q: Solve by Chain Rule y = tan ( V3x² + In(5X*))

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Q: Find the derivative of y= (2x³+x+1) 4(x²+3)5 (x4+3) 3 O A dy (4) (2x³+x+1) ³ (5) (x²+3) 4 dx 2(x²+3)…

A:

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

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A: In a differential equation where y is the dependent and x is the independent variable and the…

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Q: 1/2 x3 dx 1- V3 - 15 15 2 16 Option 1 Option 2 1 15 V15 16 8. Option 3 UOption 4 IN

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Q: Find the differential equations of every families of curves given. 1) All parabolas with axis…

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A: Solution:-

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

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Q: noExample 10; Form the partial differential equation by eliminating the arbitrary functiom f from :…

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Q: Example 10 : Form the partial differential equation by eliminating the arbitrary function f from : z…

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Q: Find 2. dy of 2.

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Q: Use Variation of Parameters to solve the differential equation. y"y tanx y C1cos xC2sin x - In secX+…

A: Result used:

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Q: determine a unique solution of the separable differential equa- tion that satisfies the given…

A: The given differential equation. dhdp=ep sinp sec3h                 h(0)=0 Separating the variables…

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Q: Find without using the Chain Rule

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

Q: 6(2tanx - x^4 + 4lnx)^1/4(2sec^2x - 4x^3 +4/x)dx. Hint: let u = 2 tanx - x^4 + 4lnx

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Q: Find the differential equation of All parabolas whose axis is parallel to the y-axis. Draw at least…

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Q: Find two positive numbers whose product is 64, and whose sum is a minimum. Solution must show the…

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Q: Find the differential equation of all family of circles in which the center lies on the line y = -x…

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Q: Obtain the differential equation of the family of curves as described. Draw some representative…

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Compute the derivative of g(x) .3 = [ 1 dt- 1+ t5 3x2 1+ x15 1+ 25x 3x2 2" In 2 1+ x15 1+ 25a 23 1+…

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Q: A flexible stretched string is constrained to move with zero slope at one end x=0, while the other…

A: Given: A flexible stretched string is constrained to move with zero slope at one end x=0, while the…

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Q: ons of the differential equations in Prob- Primes denote derivatives with respect to x 27. 3xy²y' =…

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Q: Find critical points of ƒ(x) = x² ln(x) — 1⁄x² on the interval (0, ∞).

A: Given; fx=x2lnx-12x2 ; x∈0,∞    As we know that; The critical points of the function, y=fx can be…

Q: Form the partial differential equation by eliminatiug erbitrary Goostant function from zze^ R lx-y)…

A: Partial differential equation