The family of functions -2x X- is solution of the equation y't Qy= e-x Find the constant c which de fines the Solution which also satisfies the initial condition ycs)= 1

Q: (x² + y²)dx – xydy = 0 -

A:

Q: Solve the given initial-value problem. dx y - X= = 5y², x(8) = 1 dy x(y) = Give the largest interval…

A: Given that,   ydxdy-x=5y2, x(8)=1

Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

A:

Q: Solve the given initial-value problem. dx x = 6y2, x(9) = 1 y - dy x(y) = Give the largest interval…

A:

Q: Find ø(2) for a solution p(x) to the initial value problem: 2y dx = (x2 – 1)(dx – dy); y(0) = 0 %3D

A:

Q: find a particular solution yp of the given equation. In all these problems, primes denote…

A:

Q: Q2) A:Evaluate: F(x siny – ysinx)dx dy 后后 | B: Solve the differential equation: d2- + 3 dy - 4y = x?…

A:

Q: If the function f (x) solves the initial value problem dy E (х + 1)-И dx -1/2 IT • cos(TX)

A: Givendydx=x+1-1/2-πcos(πx)

Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = = 0

A:

Q: The general solution of y" - 2y' +y= e* cos(x) is

A:

Q: Solve the initial-value problem. dy for x21 with y(4) = 4 %3D dx The solution to the initial-value…

A: We have to solve the initial-value problem: dydx=5x Solving by variable separable method,…

Q: Find the general solution of the differential equation. (Use C for the constant of integration. dy…

A: To determine the general solution of the differential equation.

Q: 2. Obtain the general solution using Bernoulli's equation. Si l + x/ dx – 6x dy = 0

A:

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ;0sx<1 ;y(0) = 1 ; h = 0.5 dx

A:

Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: If the function f (x) solves the initial value problem dy = (x +1)-1/2 – T · cos(T2) y(3) = 2 , %3D…

A: Given: dydx=x+1-12-π·cosπx Now separate the variables; dy=x+1-12-π·cosπxdx Now taking integral on…

Q: Solve the initial value problem for y as a function of x. x2 - 16 dy = X, x > 4, y(8) = 0 dx

A:

Q: Find the particular solution of (cos x x sin x + y2) dx + 2xy dy = 0 that satisfies the initial…

A: Please see the explanation below

Q: (b) Solve the initial value problem with seperation of variables and give your solution in the form…

A: Solve differential by using variable separable method

Q: 12. Test the equation for exactness and solve for the general solution. (2x - 3y) dx + (2y 3x) dy 0.

A:

Q: If the function f (x) solves the initial value problem dy = (x + 1)-1/2 – r dx - T. cos(T2) y(3) = 2…

A:

Q: The function y(x) is given implicitly by the equation y3−3xy+x3=3. Find its differential at the…

A:

Q: Solve the initial value problem given below. dy – 16xy and y = -2 when x = -4 %3D | dx

A: Given: dydx=-16xy, and y=-2 when x=-4 i.e. y-4=-2. To Solve: The given initial value problem.

Q: 3. General solution of (ylny - e-xy)dx + ( + xlny) dy = 0

A:

Q: The differential equation (xy2 + y)dy = (x + 1)dx is separable. Select one: O True OFalse

A: We have to find

Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: Solve the given initial value problem for y=f(x) 1) dy/dx=3x-2 where y=2 when x=-1

A:

Q: After separating the variables, the differential equation takes the form 2x gly) dy= 0. Compute f(-…

A:

Q: Solve the initial-value problem for yy as a function of x. (x2+49)dy/dx=1,y(7)=0.

A:

Q: 1 dy Solve the initial value problem of - 2 dx y +1 cos x , y(n) = 0

A:

Q: Solve the initial-value problem for y as a function of x. (16 – 2²) dy 1, y(0) = 7 dæ Y =

A:

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ; 0 <x<1 ;y(0) = 1 ; h = 0.5 dx

A: If dydx=fx, y, yx0=y0 then Euler's method states that  yn+1=yn+h·fxn, yn Given : h=0.5, x0=0, y0=1,…

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: Find a particular solution yp of the given equation. Primes denote derivatives with respect ס 2y" +…

A: The given differential is non homogeneous differential equation with constant coefficient.

Q: Find all initial conditions such that (x^2-x)y'=(2x-1)y has no solution, precisely one solution, and…

A:

Q: Find the general solution of DE:  1. (x-4y-3)dx - (x-6y-5) dy = 0

A:

Q: Solve the initial-value problem. (dy)/(dx) = (5)/√(x), for x ≥ 1 with y(4) = 4 The solution to the…

A: we have the differential equation  dydx=5x with y(4) = 4 having the initial value problem

Q: Find the particular solution of the equation 2(x +3) dy – xy dx = 0 %3D - tisfying the initial…

A: Given: 2(x+3)dy-xydx=0     satisfying the intial condition x=-2 and y=1

Q: 1. Consider e* – 2/x – 3 = 0, using Secant Method with initial points xo = 1 and x, = 2, calculate…

A: The given function is: ex-2x-3=0Initial points are:x0=1x1=2

Q: 3. y'(x'y-2)dx+x(x*y' + 2y° - x)dy = 0 : y(1) = 1

A: We have to find the particular solution.

Q: Find the function which solves the initial value problem dy/dx= 3ex −2x;  y(0)=−1.

A: Given that dy/dx = 3ex-2x;   y(0) = 1.dy = (3ex-2x)dx            (By cross multiplying)Integrate on…

Q: - ydx + (x ++xy )dy= 0

A:

Q: Solve the following equation to obtain the family of solutions.Show your solution. (9+y²)dx +…

A: Finding the solution of differential equation

Q: 4. Show that 3x²e"dx + (x*e" – 1)dy = 0 is an exact equation and then find the solution.

A:

Q: Determine whether the equation (ye™y . 1 - =)dx + (xe®Y + y2 is exact. If so, solve the initial…

A:

Q: Solve the given initial-value problem. dy sin(x) + (cos(x))y = 0, dx -2 y(x) = %3D Give the largest…

A:

Q: 3. Find the general solution of y"-3y'+2y = e* cos x [using variation of parameters]

A:

Q: Solve the given initial-value problem. dy X- +y=6x + 1, y(1) = 7 dx y(x) = Give the largest interval…

A:

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)x2y is an…

A: Here given differential equation as dydx=12x2yordyy=x2dx2

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.