4. Consider the one-parameter family of equations: X" + XX = 0 (a) What is the general solution when < 0? Assume X= -µ². (b) What is the general solution when A> 0? Assume A = µ?. (c) Show that the following BVP has only the trivial solution when A= 0: X" +XX = 0, X(0) = 0, X(4) = 0

Q: B. Solve x' = 01 1 54 x + 12e4t 18e4t

A:

Q: (5) Solve for n EN. +2 (a) (3) = }(n+²). 5 n (b) (²) > (^).

A:

Q: h(x) = 4(2x – 3)*(2x – 5)³ , find h'(x). Factor Fully.

A: Given query is to find the derivative of the expression.

Q: y-y1=m(x-x1) y-(-1)=4/5(x-(-1)) y+1 = 4/5x + 4/5 y=

A: The given equation is y+1 = 4/5x+4/5      y = 4/5x+4/5-1         = 4/5x-1/5

Q: tan x/4 + V3 = 0 Solve graphically in [-27, 2n] %3D

A: We have given that, tanx4+3=0;   -2π≤x≤2π Let us consider that, y=tanx4            ⋯⋯1y=-3…

Q: (x"^y2/5)20 1/4 2/5 (x' (2) 2

A: since you have asked multiple questions in single request so we will be answering only first…

Q: Find the general solution of x'"'"+2x" +x=0.

A: Solution:

Q: where y1 = e* is one of the functions in the fundamental solution set. - %3D xy" + (2-2x)y' +(x- 2)y…

A:

Q: How many solutions does x^2+bx=c have if c< -(b/2)^2?

A:

Q: Find general solution 2 1 a' = |-1 0 1 1 1 0

A:

Q: x?S(x x] =0 2 2 x Can be wpitden as s" (o)= the Solu tion is

A: Note:- You have mistakenly written it as c1e^ax + c2e^-ax. At the place of a there will be α.

Q: Solve X'

A:

Q: 1. Verify x₁ = t²x² = (' -3t 5 3t+²) and x2 = 5t 3t² -2t X. t -t-> - are solutions to

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.