y(4) + ay" + by" + cy +dy = 0, here a, b, c, d are constants. Functions e-³2, e³2 and cos(√2x) are its solutions.

Q: Show that the equation f(x) =x+3x-1%=Ø %3D has at least one solution,

A:

Q: Solve the equation using Exponential Shift (D² - 2D + 2) y = 12x³e²x O y = e (c! COSx + c2 sinx) +…

A: Answer is given.

Q: y = x10 + x3. Find y5) (1)

A: Given,           y=x10+x-5

Q: Use the method of undetermined coefficients to find a particular solution of the constant…

A: In this question, we will find the Particular solution of the differential equations.

Q: If h ( x ) = 3 x 2 − 2 x, then find h (5).

A: Let there is a function fx to find the value fa we need to substitute x=a in the expression.…

Q: a1/ ý+2Í + 27 = 8 x' e¯X sinx %3D

A:

Q: g(x) = cos(x + T) + 2 %3D

A: The given expression is gx=cosx+π+2.

Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

A:

Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

A:

Q: Q1. (a) Solve the equation dy rp

A: We have to solve given differential equation

Q: Find the first derivative of the function Y = [(x – 1)(2x + 3)]?.

A: Let us see the expansion of (a + b - c)2 formula.(a + b - c)2 = (a + b - c)(a + b - c)(a + b - c)2 =…

Q: Solve f(x)= -3 +25in(X) for -T스

A: We have to solve the problem

Q: 3. Given f(x) = -7x-8-4sin(8)- 3e-6x – 4n² then determine the defining equation of f(x).

A: To determine the defining equation of f(x) from f'(x), we integrate f'(x) with respect to x.

Q: Problem 3: Find (i) f'(x) and (ii) f"(x) of the following functions. 6x4-√x , c) ƒ(x) = e4 – 5e-5x -…

A: As per the rules of the company we can answer only the first question and rest can be reposted.

Q: Evaluate L{2t e2t sin (3t) – e3(1-1) + 3et sin (4t – 5)}

A:

Q: Let h(x)=−2x2+x+4x2+4x−1, what is h′(−5)?

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y (4) +…

A:

Q: 12 cos√(√x+4 dx

A:

Q: Find a 4th degree function that has solutions X=-4-2/3 and x=-4+2/3, x=2i and x=-2

A: See the attachment

Q: The windchill index announced during the winter by the weather bureau measures how cold it "feels"…

A:

Q: solve for y, In - y| +C = (1n|cos(x) – 1| +c)

A:

Q: Solve for X if (x)=z=r

A: The given expression xy-z=rw. We have to solve the expression for x.

Q: g(x,y) = sq root of (5xy - 3x) find gx and g

A:

Q: (x² -2x9 dy Solve The firest orler oDe

A:

Q: please solve a b

A: Sure, The system depicted in the image consists of a small body orbiting a much larger stationary…

Q: 1. (D² - 4D+5) (e² sin x)

A:

Q: Find The derivative fog : 3 Ⓒ y = (3x -x ²+1) " 0 = 3r+2 2r+3 Ⓒ ² = √√√₁+√x (3

A: According to guidelines we only need to solve the first three subpart of question no 1. Rest of the…

Q: Se²x+lnx² sin x² dx = +fe²x co 2x cos x² dx

A: