Find the solution of the initial value problem: y" +4y = u_(t) – u„(1); y(0) = 0, y'(0) = 0

Q: Find the particular solution of the first-order linear differential equation for x > 0 that…

A: Given differential equation is: y'+1xy=0 Initial condition is: y2=2 We have to solve the above…

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

A: Given the differential equation y’ = 1/x, where x > 0, we have to sketch the graph of the…

Q: Use a computer algebra system to graph the slope field for the differential equation and graph the…

A: Given Data The integral is ꭍ03 xex²dx.   Let,

Q: find the solution of initial value problem. Using Differential Equations y'+2y=xe-2x,…

A:

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

A:

Q: A mass-spring system is modelled by the differential equation u" + 16 u = 0 , and the motion starts…

A: Given that u''+16u=0   with   u0=7   and  u'0=4. Its auxiliary equation is m2+16=0. Solve as…

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

A:

Q: Convert the differential equation x by letting u₁ = x, U₂ = x', Uz = x Note: Type u_1, u_2, u_3, and…

A:

Q: A mass-spring system is modelled by the differential equation u' + 16 u = 0, and the motion starts…

A:

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

A:

Q: By using separation of variables u(x, t) = X(x)T(t), break the partial differ- ential equation ди +…

A: ∂2u∂t2 +∂u∂t +u=4∂2u∂x2            (1) To solve : Given partial differential equation by method of…

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

A: y/+1xy=0 On simplification, we get ⇒dydx=-yx⇒dyy=-dxx Now integrating on both sides, we get…

Q: What is the particular solution to the 2² +3 with the differential equation dy da 3y initial…

A:

Q: What is the particular solution to the dy dx differential equation initial condition y(-3) = 2? with…

A: here is the solution

Q: Apply the Euler-Cauchy method to obtain a numerical solution of the differential equation for two…

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. dP

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

A:

Q: Consider the first order differential equation f'(t) = dy = f(t, y); y(to) = Yo dt and describe how…

A:

Q: 1 y" + 3 y + 2 y 1+ et

A:

Q: Find all the solutions of partial differential equation 25u ôx? by variable separable %3D method.…

A: All the solution of the partial differentilal equation is(1) u(x,t) =(Ax+B)(Ct+D)    (2)…

Q: Find the partial differential equation by eliminate the arbitrary constants a,b,c for ax+by+cz=1

A:

Q: Calculate the solution to the differential equation -ry 0 with bound- dr dy %3D ary values y = 1 and…

A: We have to find the solution

Q: Find all the solutions of partial differential equation a²u = 250u Par?, by variable separable…

A:

Q: Find the particular solution of the first-order linear differential equation        y′ + y = 6ex…

A: y'+y=6ex Comparing with y'+Py=Q, we get P=1 & Q=6ex Now the integrating factor is, IF=e∫P dx=e∫1…

Q: Use a technique of integration or a substitution to find an explicit solution of the given…

A:

Q: Eliminate the arbitrary functions and hence obtain the partial differential equations:   z = f(x *…

A:

Q: This problem deals with the differential equation dx/dt kx(x – M) – h that models the harvesting of…

A:

Q: Solve the partial differential equation = 3, u(x,0) = 7edz by the method of separation of variables.

A: Solution

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: Form the partial differential equation by eliminating the arbitary function from z=xy+f(x2+y2)

A:

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: Form the partial differential equation by eliminating arbitrary function from z = e" f(x – y)

A:

Q: xy' + 2y' + 2y O with initial condition y(0) = 1

A:

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

A: Given: Z=exfx-y

Q: Use the initial condition to find the particular solution of the differential equation. Differential…

A:

Q: The formation of the partial differential equation by eliminating arbitrary function of z = 5f(x" –…

A:

Q: Find the partial differential equation by eliminating the arbitary constant from 2z=/x+a+/y+b_

A:

Q: Find the eigenfunction assuming the second case for the given boundary value problem. y" +ly = 0…

A: The given problem is to solve the given boundary value problem y"+λy=0, with the given boundary…

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: Define the term homogeneous first order ordinary differential equation.  Hence solve x2y' + xy = x2…

A:

Q: Find the solution of the differential equation that satisfiesthe given initial condition.

A: Given: The differential equation y'tanx=a+y with initial condition yπ3=a for 0<x<π2. To find:…

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.