If N(x) = sin x – sin θ and D(x) = x – θ, find the limit of N(x)/D(x) as x approaches θ. (SOLVE BY USING DIFFERENTIAL EQUATIONS)

Q: y = (C₁ + C₂x) eª + sinx+x²; y" - 2y' + y = −2 cos x + x² − 4x + 2

A: Here we find the first and second derivatives of given solution and then put in the left hand side…

Q: a2u Q15// Solve the partial differential equation дудх = tan-lx sin³y ди = y when x = 0 and u = 1…

A:

Q: Consider the differential equation, x' = f(x), vith f(x) = { 1 - x x > Compute the solution to the…

A: Given, y'=fx fx=x,x<121-x,x≥12

Q: x-1, X)1 find the generol solution of the differential eguation below

A:

Q: 1. Find the differential dy in y= 2x4-3x3-5x 2. Use differentials to find approximate values for…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation- Given that, The initial value problem is- ydydx=x-1;  y0=1 By simplifying it further,…

Q: (b) To determine To compute: The differential equaiton + x = sin 4t with initial condition x (1₁) =…

A: Given differential equation is: d2xdt2+x=sin4t . . . (1)The initial condition is: xt1=0 And…

Q: z = x siny + y sinx

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: Explanation-  Given that, The initial value problem is- dydx=x2-y2 ; y0=1 Here, The function is-…

Q: Solve the Cauchy-Euler differential equation x -2x+2y = x dx dx

A:

Q: 04- Determine the general solution of the following differential equat dy tan x. +у %3D sec х dx

A:

Q: 2. Solve the first-order linear differential equatio a. y' + 3y = e3x

A:

Q: Q4// Solve the partial differential equation a²u ди cos*x given that = x when y=0 and u=3 when x=0?…

A: The given partial differential equation is ∂2u∂x∂y=cos4x Integrating on both sides with respect to y…

Q: Verify that y=sinx is a solution to dx dy 2cos x-sin x+y and solve the 2 cosx differential equation…

A: Given Information :  Differential equation : dydx = 2cos2x - sin2x + y22 cosx  y1 = sinx y(0) = -1

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Solve the following differential eyuation x 2+ 2y = x* e** y.

A:

Q: 5. Use the properties of differential operators to solve for the product of (D+x²)(xD + 2)y

A: Given: D+x2xD+2y To find: Solution

Q: Solve the differential equati on. dz (log x) = –(log z) dx X

A:

Q: Consider the differential equation, a' = f(x), with f(x) : 1- x Compute the solution to the initial…

A: Consider the given information:

Q: Prove that the function y = ecos* satisfies the differential equation: y" + sin(x) y' +y cosx = 0

A: Find y' , y" and put into given differentiatial equation.

Q: 4. u = xz siny + yz cosx + xy tanz

A: Given,  u=xz sin y+yz cos x+xy tan z

Q: 2. Use the method of equation Uariation of parameters to solve the differential dy - k- dx² dx xez…

A:

Q: of the differential equati

A:

Q: 1) y"+ y – 2y = e" + 4 sin x + x² – x solve this differential equation from derivative operator.

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A: The given initial value problem is ;    ydydx = x-1  with  y(1) = 0 We have to determine the…

Q: (a) Form a partial differential equation by eliminating the arbitrary functions f and g from z =…

A:

Q: Show that y1 = sin x² and y2 = cos x² are linearly in- dependent functions, but that their Wronskian…

A:

Q: 5

A:

Q: For an exact equation, Show that this differential equation cos(x+ y)dx= (3y² +2y+ cos(x+ y))cdy = 0…

A: We  are given the differential equation : cos (x+y)dx+(3y2+2y+cos(x+y))dy=0 On comparing with :…

Q: Let y'=4x. find all values of R such that y=Rx^2 satisfies the differential equation. If there is…

A: This separable differential equation

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: Solve and find the limit as t approaches infinity of the differential equation: y(t) = y'' + 5y' +…

A:

Q: f f(x) = ex – e-x – 2x and g(x) = x – sinx, evaluate the limit of f(x)/g(x) as x approaches zero.…

A: Here we have, f(x)=ex-e-x-2x and g(x)=x-sinx We have to evaluate limx→0f(x)g(x)=?

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . x"…

A: Provided differential equation is a homogeneous linear differential equation with constant…

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Find the point on the curve y = x3 – 3x for which the tangent line is parallel to the x-axis.

A:

Q: Show that a harmonic function u (x, y) satisfies the formal differential equa- = 0. azdz

A: Consider the provided question, Given, ux,y is harmonic function. We have to show that ∂2u∂z∂z¯=0.…

Q: The function y(x) is defined by the implicit equation x2−√ylny=1. Find its differential at the point…

A: Differentiate both sides with respect to x and solve for dy/dx

Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that  The differential equation  To find the particular solution of the differential equation

Q: Solve the non-linear Differential Equation y"=-e xy = f(x) by explicitly following these steps:…

A: Use the following formulae, to obtain the solution.

Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

A:

Q: Solve the Cauchy-Euler differential equation on the interval (0, ∞). x³y"" + 6x²y" + 4xy' - 4y = 0

A:

Q: 5. z = yex+x Iny xey-y lnx

A:

Q: 24. What does it mean to say that dV is an exact differential?

A: What do you mean by dV is an exact differential.

Q: Find the particular solution that satisfies the differential equation and initial condition. x2…

A:

Q: Find the particular solution that satisfies the differential equation and the initial condition.…

A: To find The particular solution that satisfies the differential equation and the initial condition.

Q: Consider a differential equaUion -x2 y' = xy + xe

A: we have been given a differential equation with initial condition y(0)=0 y'=xy+xe-x2

Q: Verify by substitution that the family of functions y = -(x) sin(-3x) + cx is a solution of the…

A:

Q: A more detailed version of Theorem 1 says that, if the function f(x, y) is continuous near the point…

A:

Q: 3) 6x + sin 5x + 10 cos x

A: Given function is fx=6x+sin5x+10cosx. We have to find the linear differential operator that…