4. Solve, using the method of undetermined coefficients: y" – 4y = (x² – 3) sin 2x

Q: 2. Solve using any technique y" – 2y – 3y = sin r

A: First we find CF and then PI(by using the formula of PI of sin(ax)) and further find general…

Q: d²y Show that y = sin(2t) satisfies . + 4y = 0 dx²

A: 1) To prove the given equation 2) To find the value of w

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

A:

Q: sinh(3z+1) z2 - 5z+6 Evaluate dz, where C : |z– 2i|= 1, counterclockwise.

A: We have to evaluate ∮Csinh3z+1z2−5z+6dz, where C:z−2i=1, counterclockwise. Cauchy Goursat theorem:-…

Q: Find all solutions between 0 and 2n for the following equation:

A:

Q: Solve the following diferential equation (y-y² Inx)dx = xIn xdy.

A: First we reduce the given differential equation into standard form of Bernaulli's equation, then…

Q: Find the 3 roots of the equation x3-1.25x+0.25 using BAIRSTOWS METHOD. USE r=1 amd s=2

A:

Q: On another planet, after t seconds, Cora hurls a projectile with initial velocity vo and angle from…

A: On another planet, after t seconds, Cora hurls a projectile with initial velocity v0 and angle θ…

Q: (2y² + 3xy – 2y + 6x)dx + x(x + 2y – 1)dy = 0

A: The differential equation is given as (2y2+3xy-2y+6x)dx+x(x+2y-1)dy=0 Let the integrating factor be…

Q: B) Find the approximate roots of the following equation: f(x) = x3 – 8 = 0, on the closed interval…

A: Roots of an equation f(x): roots of an equation are those values of x for which the function f(x) =0…

Q: c) Solve 2 cos(t) = -√3 for all solutions. t integer

A:

Q: 6) Solve. y" – 4y = (x² – 3) sin 2x

A: The answer is given by using method of variation of parameters as follows :

Q: Q₁:A. Solve the ODE: x³y"" - 3x2y" + 6xy' - 6y= 10x² use the variation of parameters method to find…

A:

Q: Determine the form to be used for x when using the method of undetermined coefficients. x" + 2x = 8…

A: Given DE is  x"+2x=8sin(2t) ......(1)

Q: LX X y = Cre²x cos 3x + Cze ²xsin 3x

A:

Q: Solve (t2+4) d = (x2+36), using separation of variables, given the inital condition (0) = 6. x=6 tan…

A:

Q: (xy + 1)dx + x(x + 4y – 2)dy = 0 %3D

A: Given (xy+1)dx+x(x+4y-2)dy=0 Let the integrating factor be xαyβ Multiply both sides by xαyβ , we get…

Q: Find the form only of the particular solution. Do not solve for the coefficients. SHOW WORK. V31…

A: We will find out the required solution.

Q: Find the distance d between z1 = (8+ 8i) and z2 = (-8+ 8i).

A:

Q: solve for y, xyey+tan-1(x2+y2)=π/4

A: The given equation is

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.