(b) k(x) = |æ| + |x – 1| at c1 = 0 and c2 = 1.

Q: Find f by solving the initial-value problem. = 6x2 - 12x, f(1) = 0 f(x) =

A:

Q: Find the particular solution that satisfies the initial condition. x3y'+2y=e1/x^2, y(1)=e

A:

Q: Find the particular solution for f(x) with the given initial conditions. f''(x) = 4x3 and f'(1) = 5…

A: Given,           f''x=4x3  and f'1=5  and f0=50

Q: Solve the nonhomogeneous ODE. y" - 6y' + 9y =x²e5x

A:

Q: +] has the general solution u(x, y) = e"[f(x)+g(y)] where f and g g are arbitrary functions

A: ∂2U∂xdy+∂u∂x=0let U(H.Y)=e-yf(x)+g(y)

Q: Find the function f(x) described by the given initial value problem. f"(x) = 0, f'(-3) = -5, f(-3) =…

A:

Q: Solve the Initial value problem x' -x=8(t-2),x(0) =x' (0) =0

A: We use the Laplace transform to solve the given initial value problem.

Q: = (b) Find the solution of x' = Ax satisfying the initial condition x(0) x(t) =

A: This is a multipart question. I shall solve all the three parts for you: namely part a), b), and c).…

Q: Find the absolute maximum value of f(a) = x2- 2x +9 over the interval [0,5] The value C for the…

A: Use derivative and integration for the following question.

Q: B1(b): Solve the initial value problem : f'(x)= x!0 + 12x + 19 and f(0) = 1.

A:

Q: Find the general solution of y" – 3y' + 2y 1+e-x°

A:

Q: (a) Solve the initial value problem X'(t) : -2 1 X(t), X(0) = (Ь) Describe the behavior of the…

A:

Q: Find the general solution of F′(x) = 1/x2, x > 0 and find the particular solution that satisfies…

A:

Q: Find f(x) by solving the initial-value problem: f' (x) = 3ex + 2x2;  f(0) = 5

A: The derivative of the function, fx: f'x=3ex+2x2; f0=5.

Q: Q2 find the optimal solution of the first stage (Phase I only) of the prime LP: Minz = 2x, + x2 s.t…

A: Linear Programming is a mathematical technique to optimize the given constraints.

Q: 5. Solve y"-y'-2y = e-x+1, y(0) = 0, y' (0) = 0 by undetermined coefficients.

A: Consider the given differential equation and initial conditions

Q: Find f(x) by solving the initial-value problem: f'(x) = 3e2 +2x2; f(0) = 5

A:

Q: Find the function f(x) by solving the initial value problem. f'(x) = ex - 2x ;   f(0) = 2

A: Given : f'x = ex-2xf0 = 2

Q: (8) Find the solution to the initial value problem xy' = -2y Write your final answer as an explicit…

A: The solution is given as

Q: Find a particular solution for: y" - 3y' + 2y = te*

A:

Q: The value C for the solution of the initial value problem f'(x) = x² – 6x + 2, given that f(0) = 0.…

A:

Q: Draw the particular solution for y= f (x) given the initial condition f (-1) = 0.5 x Clear Undo…

A: Given data is : f-1=0.5 To draw the particular solution for y=fx

Q: Find the solution. xy'+ xy = 1- y, y(1) = 0 Ax=y-(1+ e!-") By =x-(1- e-) © 2y = x(1 +e-2 Dy=x-2(1+…

A:

Q: 3. Solve y' = , with initial condition y(1) = 0. y2 – 1 x3

A: It is given that the differential equation dydx=y2-1x3. Using variable and separable method to…

Q: Find f ( x) by solving the initial value problem. f'(x)=e^(x)-4x;f(0)=3

A:

Q: For x=e2 y=In 2t. find y' when x=e. O 4e e 4e O e -|

A:

Q: 2. Solve y' = 2x(x² – y), with initial condition y(0) = 1. -

A: This is first order linear differential equation

Q: solving

A:

Q: x²y = 1+ cx

A: the given equation is x2y=1+cx

Q: Q1. (a) Find the solution of. 4y-0 where the initial conditions are given as

A: our objective is to solve the differential equation.

Q: Find f by solving the initial-value problem. f'(x)=6/(x)1/2 , f(1)=19

A:

Q: Find the general solution to: 3X y^ - Gy' +Qy= x*e*

A:

Q: Find the function f(x) described by the given initial value problem.   f"(x)=0,  f'(-5)=-5,  f(-5)=2…

A: to determine.

Q: Given that y1 = 3x is a solution of æ°y" + xy' - y = x2 on the interval (0, 0), use the reduction of…

A: Concept - used the reduction of order

Q: 4. Solve the equation T2T satisfying the conditions: at ax (i) T=0 when x= 0 and 1 for all t 2x,…

A: ''Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find f(x) by solving the initial-value problem. f'(x) = 3e*- 10x; f(0) = 5 %3D f(x) %3D

A:

Q: Show that y = x (1 – e*-1) is a solution | to y" – y' + e"-1 = -1

A:

Q: Solve f, e-+ n² dt. 6.

A:

Q: The general solution of the DE y"-y" + y'- y=0 is

A: We need to factorize this equation to find the solution.

Q: Suppose M(0) is any value between 0 and k = 100. Can we say anything about long term behavior of the…

A: Solution: Given differential equation, dMdt=-rMlnMK

Q: Find the general solution of the DE below. y(1) + y “ + y“ = 0 יינ

A:

Q: The general solution of the DE y" -y" + y'-y 0 is

A: we have to find out the general solution of the differencial equation y'''-y''+y'-1=0

Q: Solve the initial value problem f'(x) = vx +,f(1) = 2.

A:

Q: Find the general solution of the ODE. y" + 4y' + 4y = x-?e-2* on (0, 0)

A:

Q: If f(x, y) = −x2 + x3 - y + 4xy + y3, then in the process of obtaining its critical points the…

A:

Q: 2. Find the solution of the initial value problem and describe its behavior as t ∞ 9. 了, -1 -3 ) 7()…

A:

Q: 1 Find the general solution of x'y" +xy' -y= x+1

A:

Q: f' (x) = +3.f(1)= %2 %3D

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.