y" - 6y + 9 y = e³ y(0) = 5, y' (0) = 0 the Laplace transform Y (s) the solution y(t) is :

Q: If the Wronskian of the DE : x'y" + xp(x)y' + 3y 0 is et Then p(x) %3D -2x O

A:

Q: By making an appropriate change of variables, evaluate the double integral I = (z + y)e= v° dzdy whe...

A: By making an appropriate change of variables, evaluate the double integralI=∬R(x+y)ex2−y2dxdywhere R...

Q: Dani has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shir...

A: We need to find the total number of different combination he can make with given pants and shirts.

Q: Prove or disprove: The differential equation x +1 if x > 0 y = if x < 0 has a unique solution with y...

A:

Q: 2. Find (a) the Fourier cosine series and (b) the Fourier sine series of (0 < x < 1) (1 < x < 2) f(x...

A:

Q: If X is an inner product space and A C X, then no decision A n A= øO A- n A£Ø0

A: Orthogonal complement of subset: Let W⊂X, where X is an inner product space. The set of all vectors ...

Q: An equation of the tangent plane to the surface x = 3 y2 - z2 at the point (8,-2,2) is: (A) (x – 8) ...

A:

Q: 2+ A, B E Mace) such that Ais normal and B is Hermi tian .Prove Th at VABI) IB |l

A: Normal matrix: A matrix A is said to be normal if A*A=AA*, where A* denote adjoint of a matrix A. He...

Q: - Use a coordinate graph to find the slope of the line that passes through each pair of points. a. (...

A: The slope of a line is nothing but its measure of steepness. It is also called the rise over run. Th...

Q: Which one of the following integrals reverses the order of integration f(z, v)dydr? 1 3-3y O a. I f(...

A:

Q: What is the common difference / common ratio of the sequence 6, 8, 12,18 What is the next three term...

A:

Q: Theorem 4 Every solution of Eq.(1.1) is bounded if A < 1. 00 proof Let {ym}-5 be a solution of Eq.(1...

A: The proof to the theorem 4 is to show that every solution of equation (1.1) is bounded if A&lt;1 Her...

Q: tind the value of the consrant (min) that makes the D-E j X dx -CyfmX) dy so (Homogeneous, exact, se...

A:

Q: Find the volume of the solid lying above the cone z = V + y² and below the sphere z² + y² + 2² = 1. ...

A: The integral can be calculated by using the spherical coordinates. The rectangular coordinates can b...

Q: Let y(x) be the solution for the DE: y (x + y +2)² If y(0) = -2, then find y() 7- 3 4 2+ O 8 JTO 3 4...

A:

Q: f (x) = { 2x + 1, if – 1 < x < 1; 3, if 2 <x < 4 ||

A: The graph of f(x)=k is a straight line parallel to the x-axis. The graph of f(x)=ax+b is a straight ...

Q: In her book Recursive Functions in Computer Theory, Péter describes the important connections betwee...

A:

Q: Find the sum of An of the arithmetic series that satisfy the given condition n= 7, a1 = 2, d = 7. Gi...

A:

Q: Parametric equations for the curve of intersection of the cylinder x² +4y? = 4 and the plane x + y+z...

A:

Q: 2 sin ø Evaluate the spherical coordinate integrals " S"S r2 sin ф drdфdв

A: Evaluate the triple integral 

Q: 4. 1 a) Find by Gauss elimination, the inverse of the matrix, 2 -1 -2 2. 421

A: Since you have asked multiple questions, as per our company guidelines, we will solve the first ques...

Q: Let A = {4,5,7} and B = {8,9}. Find A x B. Choose the correct set. O A. (32,36,40,45,56,63} O B. {(4...

A: Given that                   A={4,5,7} and B={8,9}. And we have to find A×B.  

Q: 1 Indicated a definition interval solution of the given differential equation dy + y = x + 1 dx f(x)...

A:

Q: Exercise 2. Find a formula for the curve which is traced by the motion of a fixed point on a wheel o...

A:

Q: An equation of the tangent plane to the surface y = 3 x? - z? at the point (-2,8,2) is: (A) 12 (x + ...

A:

Q: Evaluate 3zdV E where E is the solid enclosed by z = 1 and z = x + y

A: we need to evaluate the given integral about the solid E . first we will find the limit of the integ...

Q: Solve for the given system of linear equations. X+2Y+5Z = 35 2X+5Y-4Z = 12 X+Y-32 = 15 Base on the g...

A:

Q: 1. Finish the truth table then determine if it is a tautology, contradiction, or contingency. (an bL...

A: Since you have asked multiple questions, as per our company guidelines, we will solve the first ques...

Q: Let (R, d) be discrete metric space and A = N then A is complete and compact neither complete nor co...

A: Given that (ℝ,d) is a discrete matric space and A=ℕ. then     d(x,y)=0 if x=y1  if x≠y A matric spac...

Q: The solution of the differential equation In(y')=2x-y is given by

A:

Q: 4. One of the following could be a series solution for y-xy = 0 with y(0) = 3, y (0) = 0 O3- 60 90 0...

A:   Here we solve the problem by cross check the option  that is we use option elimination method .

Q: A simultaneous equations system is given by:          6y – 2 = 3x          2x + 5y = 4    Find the...

A:

Q: The volume of the parallelepiped determined by the vectors ä =,b = and č = is: (A) 12 (B) 6 (C) 24 (...

A:

Q: 14. One of the following could be a series solution for y"-xy 0 with y(0) = 3, y' (0) = 0 O 3++* +.....

A:

Q: b) A function g: Z → Zis defined by the rule g(m, n) = m + n Determine whether it is onto or not..

A: We will answer the first question as we don't answer multiple questions at a time. Please resubmit t...

Q: use power series to solue this DoE 30

A: We need to use power series to solve  (1-x2)y"-2xy'+2y=0

Q: For the straight line defined by the points (3,51) and (5, 91), determine the slope (m) and y-interc...

A:

Q: + 3y2 + x2 + 2xy. Then one of the following e a local minimum a local maximum a saddle point derivat...

A: Important key points:

Q: Let I = , zdV ,where D is bounded by the planes x = 0, 9. z = 0, x+ y = 2 and the cylinder x2 + z² =...

A: We will find out the required expression for given integral.

Q: The maximum value for the function f(r.y) = 2r + y -: subject to the constraint r+y + = 24 is A) 24 ...

A:

Q: The maximum value for the function f(x, y) = 2x + y – 2z subject to the constraint x2 + y? + z² = 9 ...

A: Note that we consider f(x,y,z)= 2x+y-2z  

Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

A:

Q: The series solution for the differential equation y''+xy'+y=0 , the recursion relation is Select one...

A:

Q: 1. Convert base-ten numeral 3 to base 3. 2. Is 103 = 3O? Yes or No? %3D 3. Fill in the blank: In the...

A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three ...

Q: Let y(x) be the solution for the DE y+ytan(x) + sin(x) 0 If y(0) = In 2, then at x= the value of y i...

A:

Q: By making an appropriate change of variables, evaluate the double integral IL (r + y) e v° dædy I wh...

A: We will find out the required value.

Q: 2. Do the three planes X + 2y + z = 4, y - z = 1, x+ 3y = 0 have at least one commom point of inters...

A: The equation of the plane is given by the formula ax+by+cz+d=0. The system of planes can be solved s...

Q: Find a particular solution to y"+ 2y'+ y = 1 (A) (B) y, = 21-1 %3D (C) y,-2r-2 Y, = (D) y, =1 (E) y,...

A:

Q: The plane 6x + 8y + 60z = 700 intersects the cone z? = x? + y? in an ellipse. The sum of the z-coord...

A:

Q: Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element...

A: The pivot column in the simplex table is determined by the most negative value of Zj-Cj, the last ro...

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.