Let y be the solution of the initial value problem y" +y = - sin(2x), y (0) = 0, y'(0) = 0. The maximum value of y is

Q: 5. Show that the differential equation y" +a²y = f(x), y(0) = y'(0) = 0, has 1 y(x) = -…

A: proof:-we have          y(x)=1a∫0xf(t)sina(x-t)dt   ⋯(i) differentiate by leibnitz's rule(i) , we…

Q: 3. Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď²…

A:

Q: Show that the first order differential equation (x + 1) y' - 3y = (x + 1)5 is of the linear type.…

A: To solve x+1y'-3y=x+15; y=1.5 when x=0

Q: Find the particular solution of the differential equation √x + √y y′ = 0 that satisfies the initial…

A: x+y y'=0x+ydydx=0ydydx=-xydy=-xdx

Q: from the partial differential equation by eliminating the arbitrary function z=(x2+y2+z2)

A:

Q: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

A:

Q: determine the general solution of the given differential equation that is valid in any interval not…

A:

Q: r -t = sin 2x cos 3y + (x + y).

A: In this question, we solve the non-homogeneous partial differential equation by the operator method.

Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: Form the partial differential equation by eliminating the arbitrary function z =x+y+f(xy)

A:

Q: Find the particular solution of the first-order linear differential equation    y′ + (2x − 1)y = 0…

A: the given differential equation is y'+(2x-1)y=0. y(1)=2

Q: Verify for a > 0, that y = is a solution of the nonlinear differential equation yyll = x.

A: The function is a rule that associates or fixes a number to the particular point x. If , then the…

Q: Use the slope field for the differential equation y′ = 1/y, where y > 0, to sketch the graph of…

A: Given the differential equation                                              y'=1/y where y>0

Q: 9. The characteristics of the partial differential equation *3 = 0 ду a əx dy +2- дх ду + cos? when…

A:

Q: Use variation of parameters to to find the general solution of the non-homogeneous Euler-Cauchy…

A: To Determine :-  Use variation of parameters  to find the general solution of the non-homogeneous…

Q: 3. Find the general solution of differential eguation y" - v' - 6y = 0

A:

Q: form the partial differential equation by eliminating the arbitrary function from z=xy+f(x2+y2)

A:

Q: 1. (2x + y – 1)dy + (4x + 2y – 3)dx = 0; when x = 1, y = 2

A:

Q: Solve the differential equation (3xy+y2)+(x2+xy)y′=0 using the integrating factor μ(x, y) = (xy(2x +…

A: The differential equation is 3xy+y2+x2+xyy'=0.

Q: 2t°y'+3ty-y=! t.

A:

Q: x*in(x)dx (y1 21)dy = 0

A:

Q: State where in the ty-plane the hypothesis of the (non-linear) Existence and Uniqeness Theorem is…

A: Given: The given differential equation is y'=t-y2t+5y

Q: Show the stability behavior of the stationary point z = 0 of the differential equation Y = By° in…

A: For the solution follow the next steps.

Q: Solve the initial value DE y' - ytanx = sinx, y(0) = 1 5-cos 2x 5-cos 3x 5-c A) y B) y = с) у %3D 4…

A: Given differential equation is y'-ytanx=sinx,   y0=1 Compare the given differential equation with…

Q: 3. Approximate the solution to the partial differential equation a²u ²u 5л 0x2 (x, y) + dyz (x, y) —…

A: Given: ∂2u∂x2x,y+∂2u∂y2x,y-12.5π2ux,y=-25π2sin5π2xsin5π2y To find: Dirichlet boundary condition

Q: c) Show that y, = x* – x² Inx over the interval (0, 0) is the particular solution to the…

A:

Q: What is the solution of the partial differential equation Da :=xe O d. := cos(x- y) 2=sin(cos(xy))

A: Let's check for z=xeyx ∂z∂x=xeyx-yx2+eyx=-yxeyx+eyx And, ∂z∂y=xeyx1x=eyx

Q: Find the general solution of non-homogeneous differential equation for y"+3y'+2y = 2020x which…

A: The differential equation is given as y''+3y'+2y=2020x Corresponding homogeneous differential…

Q: Suppose that one solution y, (x) of the homogeneous second-order linear differential equation y"…

A: This can be evaluated as follows:

Q: determine the general solution of the given differential equation that is valid in any interval not…

A:

Q: The transversality condition holds for the partial differential equation X4x +Uy=0 with the initial…

A: In the given question we have to check the transversality  condition of the given P.D.E s.t xux+uy=0…

Q: 4.Calculate the differential equation y''= 3x + y2 + y + y', y (0) = 2, y (1) = 4 by shoot-ing /…

A: Given that the differential equation is  y''=3x+y2+y+y'; y(0)=2, y(1)=4 Also given that h=1/3 we…

Q: Solve for the solution of the given Partial Differential Equations with boundary conditions. Əri =…

A:

Q: Find the integral surface passing through the curve 1 T: z = sin y + e' +- x = 0 8 of the partial…

A: In this question, we solve the partial differential equation by using the surface condition.

Q: Example Find the solution of the differential equation x'+y² 2ху dy dx that satisfies the condition…

A: given,

Q: y' +y = 0

A:

Q: 3] Form the partial differential equation by eliminating arbitrary function from z = e® f(x – y) -

A: Given: Z=exfx-y

Q: Find a particular solution Y of the nonhomogeneous differential equation y'' + y' + y = 2 cost −…

A: Given a nonhomogenous differential equation y''+y'+y=2cost-sint

Q: Find the general solution of the equation by looking for a special solution of the homogeneous part…

A:

Q: Find the general solution of the second order homogeneous partial differential equation r-t = sin 2x…

A:

Q: Form the partial differential equation by eliminating the arbitrary constants a and b from z = ď² x…

A:

Q: x²u = x sin y Uyy

A:

Q: Discretize the differential equation y " – 3y' – y = -3t, y(-1) = 0, y(1) = 0 with step-size h %3D

A: Given: y''- y' - y =-3t, y(-1)=0 and y(1)=0 with step-size h =25

Q: determine the general solution to thegiven differential equation. Derive your trial solution…

A: Given: y'''+3y''+3y'=y=2e-x+3e2x To find: General solution of the given differential equation.

Q: Find the particular solution of the differential equation (2xy - sin x)dx + (x² - cos y)dy = 0, when…

A: Exact differential equations

Q: Determine the solution of the differential equation y*y' = 4x² met die beginvoorwaarde dat with the…

A: As per our guideline,we are supposed to answer only one asked question.kindly repost other question.…

Q: Suppose the motion of a mass-spring system is described by the differential equation x"+By'+1y=0.…

A: We will use knowledge of basic differential calculus to solve this problem.   It should be noted…

Q: The particular solution of the differential equation y y- 2y = sin3x is: y(x) =Ce3x+Ce3O…

A:

Q: Determine the location and type of all equilibrium points for the nonlinear differential equation…

A:

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.