3. For the initial value problem: x(x- 1)y" – 3xy" + 6x²y' - (cosx)y = Vx+5 y(x,) =1, y'(x,)= 0, y"(x,) = 7 Pick a value for x, such that the existence and uniqueness theorem can guarantee us nothing. Then pick a value for x, such that we are guaranteed the existence of a unique solution and state the interval on which it is guaranteed.

Q: i) Find the tangent and normal lines to the curve r*y° +sin(xy)+ln(1+y)+sin(2x) = sin(2) at the…

A:

Q: Q.2) The basts of the equatioon y'' + y" = 0,are: b) 1,1.e a) 1,1.e c) 1, x,e²* d) 1,x.e" 0 about

A:

Q: (12) If y = a X"-b X*+1+5 is a polynomial and a » bER , then may by represent dX" by one of the…

A: n order derivative

Q: a) m - 1 b) m – 2 Q.8) The characteristic equation for y"" + 3y" – 4y = 0 , is : b) 2' = 32?-4 c) m…

A: To find out the characteristic equation.

Q: One of the followings is a harmonic function O a. u(x,y)=(x' - y' – 2x+1), O b. u(x,y)=(x-y - 2x+1),…

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Q: (1) (II) 10 F. 10 +t 10 10 -10 -10 (II) (IV) 10 10 斗t 10 t 10 -10 -10 a) y = 10e-t/2 cos 2nt b) y =…

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Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

A:

Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: E Let C₁ be the curve parameterized by r(t) = (cos² t, sint) where t = [-]. Let C₂ be the line…

A: Given that C1 is the curve parameterized by r(t)=(cos2⁡t,sin⁡t),t∈[−π2,π2].Let C2 be the line…

Q: 14. If f(z) = 2 + ² -r', then the equation S(z) = 0has a solution on the interval A [1,2] B (0,1] c…

A: Given equation, fx=2+x2-x3, To find the interval on which the equation fx=0 has a solution.

Q: 4. Determine all possible functions f(x) that satisfy the given conditions. (a) f'(x) = V¤ – 3 x2…

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Q: Q.4) The Wronskian W(e~2", e",e²), is: a) 12e b) –12e c) 6e² d) -6e"

A:

Q: f(x) = In (x² + 1) %3D Note: 2x and f"(x) = 2(1 – x)(1+ x) (x² + 1)² f'(x) %3D %3D x2 + 1 (a) Find…

A: Here, we are going to solve the first two subparts and for the remaining subpart please post the…

Q: Which of these functions (or none of them): (1) z=e" (ycosx-xsiny) or (2) z=e' (y cosx-xsin x) 0²z…

A:

Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

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Q: 4 a. Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: a. Verifying Conditions of Cauchy-Picard Theorem  b. Estimating the Interval of Existence

Q: Let h be the function with derivative defined by h'(x)= x³-8x² + 12x. At which of the following…

A: Let h be the function with derivative defined by h'x=x3-8x2+12x To determine the value of x  where…

Q: 4. Suppose the following functions are a general solution of: y(4) + azy" + azy" + a13 + a0y = 0…

A: The differential equation is y(4) + a3y''' + a2y'' + a1y' + a0y = 0 We have to find a0, a1, a2 and…

Q: 24. Is there a value of b that will make r +b r 0 differentiable for all real numbers? (a) b = 0 (b)…

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Q: i) Given that f(x)=3cos5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a <90°.…

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Q: If z=xtiy where x and y are real, find the real and imaginary parts of:- Z-1 Z+1 ピージ (x+アア 2.xy…

A:

Q: Find the GS for y""+y"+y' + y = 1−x + e* - COS X

A: Given differential equation y'''+y''+y'+y=1-x+ex-cosx

Q: f, (3,5) and fy (3,)us(«, y) = |and f, (3,) if f (x, y) = (b) Find x² sin(y) – Ax-3 10 CLO-2 Where A…

A: The given function is  f(x, y) = x2. siny - Ax-3

Q: 5. Find L{f(t)} a. f(t) = sin?(t) + t b. f(t) = n² – 8e¬2t + (et + 1)² | c. f(t) = F, sin yt -cos…

A: As per our limit we can solve only first three subdivisions if you want the answer for other…

Q: 07/ Express in the form x + jy (1) e'(x/2-j) (2) In(3 – j) (3) sin(r/4+ j2) -

A:

Q: 1. ('88 BC) The length of the curve y = x³ from x = 0 to x=2 is given by 2 2 A) [√₁ + x ²dx (B) √ √…

A: Given,.Formula for length of the curve is,

Q: 2. Determine whether sin x or cos x is a solution to y" - 2(cot x)y' + (1+2 cot² x) y = 0 Hence use…

A:

Q: If New Hampshire's population was 1.4 million in 2018 and there were 1.3 million motor vehicle…

A:

Q: 11. In 1970 the Department of Natural Resources released 1000 splake (a crossbreed ofE fish) into a…

A: The Malthusian growth model is P(t) = P0ert, where P0 is the initial population.

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.