If we use the Laplace transformation, the solution y(t) of the following differential equation: y' + 2y = 1, with y(0) = 1 will be transformed to Y(s) such that

Q: (b) Use the substitution x = e' to transform the Cauchy-Euler equation x²y" – 4xy' + 6y = 3x² +…

A:

Q: For linear differential equations with constant coefficients, Laplace transforms Lly"] is Ly'1-Y…

A: Third option is correct.

Q: Determine whether the given differential equation is separable. (xy* + 8y*) dy - 2ydx = 0

A: Given: To determine whether the given differential equation is separable.

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: From the figure, the critical points are 1, 3 and 5. Thus, f(y) should contain powers of (y-1),…

Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y'…

A: we have to find solution by using laplace , we know that  LY'=YS-Yo LY=YS L1=1s

Q: Given the differential equation y'' – 2y' – y = 0, y(0) = – 1, y'(0) = 0 - Apply the Laplace…

A:

Q: 5. In the differential equation 2.xydx+(y² – x dy=0, what is 1 (OM ON M dy

A:

Q: The value of the constant a such that the given differential equation is exact ) 1 1 dx + 1 dy = 0…

A:

Q: and the differential equation M (x, y)dx + (sin x cos y – xy - e-)dy = 0 is exact. |

A: It is exact differential problem

Q: If we use the Laplace transformation, the solution y(t) of the following differential equation y' –…

A: using the laplace transformation LY'=SYS-y0 LY=yS L1=1s

Q: Use Laplace transforms to solve the differential equation: y' +y – et = 0 where y (0) = 0, y (0) = 0

A:

Q: Use Laplace transform to solve the differential equation y"-2y'-3y=0 with the initial conditions…

A: A linear homogeneous ordinary differential equation can be solved using the Laplace transform apart…

Q: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

A: What is the solution of the differential equation using Laplace Transform y'' - 3y' + 2y = e3x when…

Q: dy et-y + et + eY + 1 dx

A:

Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y' –…

A: The given differential equation is                                       y'-3y=1  with  y(0)=2.

Q: y - 5y = 0 with an initial value of y(0) = 2. Solve the above linear differential equation using…

A:

Q: Given the differential equation and its initial conditions y" + y' = 12 + 2 with y(0) = 1 and y'(0)…

A: Take the Laplace transform on both sides of the differential equation.

Q: Suppose that a certain population has a growth rate that varies with time and that this population…

A: First rearrange terms in the given ordinary differential equation  dyy=0.5+sint5dt since it is…

Q: (b) Consider the differential equation ydx + x(lnx-lny - 1)dy = 0. Hence, or otherwise, use an…

A: Let us consider a differential equation of the form Mdx+Ndy=0 To equation is exact if ∂M∂y=∂N∂x then…

Q: 1. Given that y satisfies the differential equation ,dy +22+y 0, use the approxinmations dx Yas -2y,…

A:

Q: Consider the following system: Y =-K dK =1- pK dt I= i(t)Y where a and p are constants and K , Y , I…

A: The solution are next step

Q: 4) dx Solve the differential equation dt under the initial condition x(0) = M – 2 by Мx — ЗеМt using…

A:

Q: Use Laplace transform to solve the differential equation -2y + y = 0, with the initial condition…

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: (b) Use the substitution a e' to transform the Cauchy-Euler equation a*y" – 4xy' + 6y = 3x + In(a"),…

A:

Q: Find the function y=f(t) passing through (0,6) with the given differential equation

A:

Q: Find the general solution y(t) of the differential equation given by y" + (3')? – 2 el-3) = 0 using…

A: Rewrite the terms to get simplified version so that the differential equation is solved easily.

Q: 1. Solve the differential equation for y= y(t) given the initial condition. dy 1 dt ty – y with y(2)…

A:

Q: Draw a direction field for the given differential equation and determine the behavior as ?→∞. If…

A: Given: y'=y+e-t

Q: Consider the ordinary differential equation y'' + 4y'+2y=0 such that a solution is of the form y and…

A:

Q: At any given temporal coordinate, the rate of change at which the vertical position of an object…

A:

Q: In the differential equation (x + 2y - 1)dx + (2x + 4y - 3)dy = 0 , we let the substitution w =…

A: Substitute w=x+2y

Q: (i) Form the partial differential equation by eliminating the arbitrary function from the following…

A: Elimination of the function, using partial differential equations

Q: 4. 2ydx + (x - a* y³) dy = 0

A:

Q: What is the type of the following differential equation? y’ + (2xy+y)/2 = 1/e2x   Seperable Exact…

A:

Q: 1. Construct a slope field for the differential equation = dy x + 2y dx

A: The given differential equation is: dydx=x+2y So the slope at any point (xo,yo) will be given by…

Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: What is the differential equation obtained by eliminating the parameter A from the 21 relation y = A…

A:

Q: Find the differential equation by eliminating the arbitrary constant "a" from the family of…

A:

Q: Let c be a constant. For the following differential equation: dy - y = x dx In which of the…

A: Given differential equation is dydx-y=x      1 We know that Isoclines are given by putting the…

Q: 1. y' = et ; y(0) = 2

A:

Q: Given the differential equation y'' − 3y' – 4y = - 2 sin(2t), y(0) = 0, y'(0) = - = - 1 Apply the…

A:

Q: 3. Consider the following system of differential equations: where y(0) = Find the solution of the…

A: 3. We have  y˙=01-12y+04ex       y(0)=3-2x˙y˙=01-12xy+04exx˙=yy˙=-x+2y+4exlet  L(x)=F(s)…

Q: How does the following differential equation (y+2xy*) dx + (1+ 3.x²y² + x) dy = 0 satisfy the…

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: B) Solve the differential equation by using Laplace transform y" - y = -t² y(0) 2 and y'(0)=0

A: The given equation is;  y''-y=-t2, y(0)=2, y'(0)=0.

Q: Use Laplace transforms to solve the differential equation y' + 2 y = 10 e3t , if y(0) = 6

A: The given equation is: y'+2y=10e3t,y(0)=6...(1) Taking Laplace transform on both sides of equation…

Q: If we use the Laplace transformation, the solution y(t) of the following differential equation: y' -…

A:

Q: Find the general solution of the first-order linear differential equation (y + 1) cos x dx − dy = 0…

A: We have to find general solution of the first-order linear differential equation: y+1 cos x dx-dy=0…

Q: Solve the given differential equation (where the function is subject to the given conditions) by…

A: Solve the given differential equation (where the function is subject to the given conditions) by…

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.