- While working with a colleague you encounter the following initial value problem: dy (2² – 9) - In(z")y = e", y(1) = -2. – In(a*)y = e**, y(1) = -2. %3D dx After working on this problem for a minute, your colleague states he found a solution with the property that lim y(z) = 0. Explain why your colleague has not correctly found a solution to the initial value problem. %3D 00

Q: Find dy/dx for each of the following. Do not simplify your answers. 3 (a) y = 3* – 3x7 + cot(3x³ +…

A: Part(a) Given

Q: 6) Solve for y: 3"*1 = 9"-1

A:

Q: Given f''(x) = – 9 sin(3x) and f'(0) = – 4 and f(0) = 5. %3D %D Find f() =

A:

Q: D. Exponential shipting Theorem (D°+ 10* - 30 - 18) y = 24 x ° e-s* -3x 4.

A:

Q: If I = , 2x e*dx dy = then 1=

A: Given:     ∫11∫012xex2dxdy

Q: (7) coshx + sinh x = e* %3D

A:

Q: 4 3 f(x) = arcsec %3D f'(x) =

A: First simplify the given function than use chain Rule of derivative.

Q: 4. [csch(x)] = -csch(x) coth (x) dx

A: we know thatdifferentiation of cosh(x) is sinh(x) and vice- versa

Q: 3. If f(x) X-x find F(tanx) 1+x2

A: 7.The given limit is: limx→-∞x23x2-4x+1 To evaluate the value of the limit.

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A: Given: y=tanx+1x To find: y' Solution: Quotient rule of differentiation states that,…

Q: x* + 4 dx : %3D 3

A:

Q: If x2+y2-2axy=1  then find (dy/dx)

A:

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: 2. Find dy/dx: a. 3x? – (xy²)½ = 2y³ b. у%3D (сosx — ях)4x*

A:

Q: Solve the Bernoulli's equation dy/dx −1/2(1+ 1/ x)y = (3 /x)y^3

A:

Q: y = (cos x-x4+ 1/x2)5 - In (3x+1)  Find dy/dx

A: =?

Q: Once you hit the p.i = ... What is the Yp solution you are following to apply the 1/d^2 +4…

A:

Q: Given f''(T) 9 sin(3r) and f'(0) 6 and f(0) = 3. Find f 2.

A: Given f"(x)=-9sin(3x) and f'(0)=-6 and f(0)=3

Q: Given f''(x) = – 9 sin(3x) and f'(0) - 2 and f(0) = 4. (E) = Find f

A:

Q: 1-3x2 2. (1– x²)dy + (3*) ydx = dx %3D

A:

Q: Classify and Solve the following x(dy/dx) + 4y = (x^4)(y^2) subject to y(1) = 1

A: