1. Find the maximum and minimum points of the given equation: a. y = x3 - 3x b. у%3D (x - 6)?(9— х)

Q: Find the general solution for the equation: dy=(x^2+x)y^3dx

A: Given:          dy=x2+xy3dx

Q: and the net is decribed by the equation y = V1 – x2 – z2, y 2 0,

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Q: ty (t+1)y + y = t²

A: Given That : ty"-(t+1)y'+y=t2 To find: solve the differential equation using determinant coefficient…

Q: Suppose a cheetah is dashing due north at a rate of 30 m/s toward a popular watering hole, and a…

A: We need to find x(t),y(t),r(t) in the above question.

Q: Find the solutions to y = −2y + 8 satisfying y(0) = 3 and y(0) =4, and sketch their graphs.

A: The given differential equation is y' = -2y + 8, satisfying the initial condition y(0) = 3, y(0) =…

Q: If y = f(x) is the solution of y' – 3y =-12.e 9z, f(0) =1, then

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Q: Find the formulation of a particular solution of y" + 3y' +2y = 3+t2 – te-2t cost without…

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Q: Find the particular solution of y' = xey-x? given y(0) = 0.

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Q: (c) xy' = y(3– x)

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Q: Find the general solution of the given equation y" + y = 0

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Q: The x coordinate of the point of intersection between the two curves Y e14a and y = 1 is = x =

A: Given: y=e14xy=1

Q: dy-Hy-5 te %3D xp

A:

Q: If the depth is given by the equation z = 3x2y + xy. The equation of the cut-off curve when y=1 is?…

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Q: Solve using variation of parameters or reduction of order (D² – 3D + 2)y = (1+e²x)¯2

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Q: (a) For the solution that satisfies y(0) = 0, sketch the solution curve and estimate the following:…

A: (a) The solution curve with the direction field that satisfies the initial solution y0=0 is as…

Q: Solve the non-homo. D.E. 1.y" + у%3D Зе2x

A: Differential

Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: Solve the following equation by using separation variable method: y(x,0)=10 t> 0 y, (0,1) = y,(7,t)=…

A: The given problem is to solve the given partial differential equation with given initial conditions…

Q: Use the explicit Euler method to plot the  estimate y(2) if y(t) is the solution to y' = t - y3 with…

A: Given IVP is y'=t-y3, y(0)=1 we have  f(t,y)=t-y3 Here using n=10 steps, Then step size h=upper…

Q: Use variation of parameters to find the particular solution to 3t y'' + 5y + 4y = 2e Y(t)=| Preview

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Q: Find the minimum speed of a particle with trajectory c(t) = (t3 – 4t, t2 + 1) for t > 0. Hint: it is…

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Q: The non-homogenous solution of the following equation by using variation of parameter method y" +y =…

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Q: If y = sin 0 + 5, what is the minimum value of y? a) 4 b) 5 c) 3 d) 8 e) 11

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Q: Find the solution for: y' – x e = 0 using separation of variables.

A: Solution of differential equation

Q: Find the minimum speed of a particle with trajectory c(t) =(t 3 − 4t,t 2 + 1) for t ≥ 0. Hint: It is…

A: Given a particle with trajectory : c(t)=(t3-4t , t2+1)    for t≥0 We need to find the minimum speed…

Q: An isolated bar is kept at zero temperature at its ends. If it's given initially temperature, f(x) =…

A: First of all the question has a small error in place of (dt) (dx) was printed. Which I had corrected…

Q: a) (x² + y² + z²)² = xyz %3D

A: see the attachments below

Q: (D² + 1)y = sec² x csc x X cSC X

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Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Find the solution to the Bernoulli Equation. 2x³y = y(y? +3x?)

A: The solution is given as

Q: Solve for the particular solution: dy + 를y3D -2°y"; y(-1) %3D2 dz

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution :-

Q: Solve for the particular solution: dy = y + Vr2 – y?, y(2) = 0 %3D - da

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Q: Find the minimum speed of a particle with trajectory c(t) = (t3 − 4t, t2 + 1) for t ≥ 0. Hint: It is…

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Q: (b) For the solution that satisfes v(0)1, sketch the solution curve and estmate the following v(0.5)…

A: (b) The solution that satisfies y(0) = 1 can be sketched as follows:

Q: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

A: If the depth is given by the equation z = 3x2y + xy , the equation of the cutoff curve when x=1 is?…

Q: y = mx + b is called the v ---Select--- rm of the equation of a line. standard Additional Materials

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Q: 5. Give the graphical significance of the constant a for the equations of the form y-a(x-h)²+k.

A: We have to discuss the graphical significance of given equation.

Q: Obtain the general solution to the equation. dy y + 7x +1

A: Here we have to find general solution of differential equation

Q: 1 + 12 8x*' - Find the length of the curve y= 1<x<2. 4

A: y=x612+18x4 Differentiate the  above equation dydx=ddxx612+18x4dydx=x52-121x5

Q: (B) Find the subsequent displacement for a simply supported beam of length (L) take a positive value…

A: The given equation: Where C is a constant. This is the function of Y(t, x). To find the…

Q: B- Solve the D.E.: y--e* = 0, y(1)=1 .

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Q: ,2 y² e2y dy = e2y 2 (y² y + C 4 2

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Q: let y"(x) + y(x) = 0 be given What would be a suitable solution y(x)?

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Q: Sketch an approximate solution curve that passes through each of the indicated points

A: Here is the solution of the given problem.

Q: H.w Solve y'+y'-zy= -2 f yoj=Zfylcojal

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Q: For what values of m does Y = emx satisfy Y" + Y' - 2Y= 0 ?

A: For what value of m does Y=emx satisfy Y''+Y'-2Y=0

Q: Supply the missing steps on equation below x•dy (x² + y² ³/2 Hol 2a B 47 xVx² +a² -a

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Q: Solve the bernoulli's equation x(6x^2−y−1)dy +2ydx =0.

A: The given Bernoulli’s equation can be written as: