The general solution of y" +4y" +5y'+2y 0 is (a) Ae-2* +(B+ Cx)e¯* Ae* +(B+Cx)e2* -2x (b) (c) Ae 2* +(B+ C)xe* (A+ Bx)e* +(C+ Dx)e²2r -2x (d)

Q: Which of the following functions is one - to - one? A h(x) = x³ – x² –2x B (x)=|2x – 1| © f(x) = x²…

A: 1) for a one to one, function, or any value in it's domain there will be a unique value in it's…

Q: 3y3 (2y+3) (y-5)

A: The given expression is

Q: (5 + y)(4 + y) = (6x + 2y – 4) + (2x + 2y + 10) = (x – 3)(x + 3) =

A:

Q: Js:(Jī - x*) dz = 15/x (A) vX - 15x? +C 2 (B) 5x - 3 + C 4 (C) 2x5/2 _ 5x + C 4 (D) 25x5/2 5x1 + C 4…

A: Given: ∫5x(x-x2)dx

Q: (2x)(x-y+5)(5y)

A: Firstly, we multiply 2x by each term of x-y+5

Q: How do I write x2 + y2 + 8y + 2 = 0 in standard form.

A: Given,

Q: csc -1Vxdx (6) Vx3 -x2 CSC x3-x2

A: From the given problem:   I=∫csc-1xx3-x2dx   So we can also write as:   I=∫--2csc-1x·12x-1xdx.....1…

Q: 9(x) = 2x + 3 (a) g(5) 6.

A:

Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

A:

Q: x² +25 D)+ Xx Evaluate the following integral f (6) A) 4 Inx-21-In/x+31+ C C) 4 Inx-31-In/x+21+ C…

A: We use partial fractions to solve the given integral.

Q: (x-3)-(-8x)/(x+1)+(x+1)x

A:

Q: the indicial equation of the differential equation xy'' -x2y'+(1+2x)y=0

A: Question from differential equations.

Q: (10x-19) (3r + 2) (5x-3)

A: We will use the exterior angle property of a triangle that states that an exterior angle is equal to…

Q: e) Solve [(-x'y)² + (x²y)³]²

A:

Q: (e) 7 x² 3x2-6x x²-4x+4 (f) 1−4+1/2/2

A:

Q: Expand and simplify. (a) 4(x + 3) + 5(2x - 1) (b) (x + 3)(x- 5) (c) (2x – 1)(3x + 2) (d) (a – 2b)(a…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Prove that ax² bx C (x-a) (x −b) (x −c) * (x − b) (x − c ) + x = c + - x³ (x-a)(x-b)(x-c) =

A:

Q: A(x)=x3-7x2-16x+112,(x-7)

A: Given:     Ax=x3-7x2-16x+112 , x-7   Divide the leading term of the dividend by the leading term of…

Q: x= -(b) +(b^2-4(a)(c) 2(a) x^2 + 10x - 25= 0

A: Given,         x2+10x-25=0We know that,         For the quadratic equation ax2+bx+c=0, then the…

Q: Find ify= xln(4x +1)

A:

Q: 3(x+ 7) > 2(2x + 8)

A:

Q: (x+2)(y-2)=(x-9)(y+5)

A: Open the bracket, we getxy - 2x + 2y -4 = xy +5x - 9y -45

Q: (x + y + z)(3x - 2y - z)

A: we have to solve: (x + y + z)(3x - 2y - z)

Q: 5[3m - (m + 4)] > -2(m - 4)

A: topic:- algebra

Q: 1f fC)-3x-4 -ndg)=2びナx, find slfk)

A:

Q: If fx) = (1 - x)² and g(x) = 3 - x, find fg(x)) and g(fx)). fg(x)) = g(fx)) =

A:

Q: √4x²(x³-5)ª dx = Ox³(x¹² - 25x¹ +250x6 - 1250x³ +6250) + c 12 15 O 16(x³ - 5)4 + c ○(x³ - 5)5 + c…

A: To evaluate ∫4x2x3-54dx Formulae used d(xn)=nxn-1d(constant)=0∫xndx=xn+1n+1+c

Q: 3(x+2)(x-2)=0

A:

Q: If y (x25x-1)e2x then y (3x2-10x+7)e2x O (2.7x+4)e2x O(22+ 12x + 3)e2x (2x+5)32x (2x 52-1

A: Given,

Q: Compute the cycle index for the number of non-equivalent graphs with 6 vertices. How many are there?

A: Given:-                 Compute the cycle index for the number of non-equivalent graphs with 6…

Q: f(x) = 4 − 2x/(x + 1)(x + 3)(2x + 1) = A/(x + 1) + B/(x + 3) + C/(2x + 1) find the values of A,B,C

A:

Q: (x) = - 4x2 + 2

A: We will find out the required values.

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.