1, 0 < x < 1 y" + 4y = g(x), y(0) = y'(0) = 0 where g(x) = -1, 1< x < 2 0, x > 2

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: A normal is drawn at a point P( x,y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A:

Q: A There is no correct answer from among the given choices. differential equation by separation of…

A:

Q: Eliminate arbitrary functions and hence obtain partial differential equation y =f(x – at) + xg(x –…

A: Differentiate y=fx-at+xgx-at+x2hx-at with respect to x and t, to obtain ∂3y∂x3, ∂3y∂t3, ∂3y∂x2∂t and…

Q: dy sin x 3) dx y=2cos sin x- 1 of first order linear differential equation COSx COsx y(7/4) = 3/2…

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&lt;121-x,x≥12

Q: 2. Find the differential equation of the family of curves as described below. a. Family of circles…

A: As you asked multiple question I solve only the first one 2.a) We have to find out the differential…

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: 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: 1. Verify that for constant C the function ø(x) = + Cx is a solution of the differential equation 2…

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Q: From the partial differential equation by eliminating the arbitrary functi on s f and g from = z =f…

A: Given: z=fx+ct+gx-ct

Q: 2. Using Euler's method with N = 8 and 10. dx/dt = 1 + tsin(tx), x(0) = 0

A: Given dxdt=1+tsintx  and x(0)=0 and N=8, N=10

Q: 1 of these 2 differential equations: dx dy O and (2x sin y +y) dx + (x² cos y + x)dy = 0 What are…

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Q: Determine the general solution and the particular curve that goes through point (0,0) of the e* cos…

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Q: 1. Consider the ordinary differential equation = (1-x-¹)y, with the initial values x = 1, y = 1.…

A: The fourth order Runge-Kutta method uses the following formulas to approximate the values of y at…

Q: Find general solutions of the differential equations . Primes denote derivatives with respect to x…

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A: Solution:-

Q: a particular solution that satisfies the differential equation F'(x)=3x^2 +2x -1 and the inital

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: verify that the given equation is a solution of the differential equation.(elimination of Arbitrary…

A: The solution is given as  y=-cos(x) ln(sec(x)+tan(x))                   (1) Differentiate equation…

Q: A nomal is drawn at a point P(x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: Equation of normal at the point P(x,y) to the curve is Y-y=-dxdy(X-x). ⇒X=x+ydydx Thus,…

Q: Use Euler's Method to find a numerical solution of the differential equation dy y 3+ dx With initial…

A:

Q: If y = f(x) is a function satisfies the differential equation f'(x)x³ + f(x)3x² = x³ ,where C…

A: We have to solve the given differential equation and find f(x).

Q: 7. Find the differential dy of the function y = x (1-cos(x)). If the error in x is ", find the error…

A:

Q: Consider the differential equation dy dx with a particular solution y = f(x) having an initial…

A:

Q: Find the particular solution of the differential solution dy/dx=x^2(y+2) given that the point (0,5)…

A: Given,  The differential equation  dydx=x2y+2   Point 0, 5 lies on the graph of the solution  We…

Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation.

Q: Find the differential equation (Eliminating Arbitrary Constant)(Family of Curves): Strophoids :…

A:

Q: 5. Obtain the differential equation of the family of circles with center at point (h,k) and radius…

A: Please refer to the image below

Q: Eliminate the arbitrary constants from z= (x-a)^2 + ( y- b)^2 to form the partial differential…

A:

Q: The differential equation governing the velocity of an object is dv = -kv", dt where k > 0 and n are…

A: The given differential equation is dvdt=-kvn, where k&gt;0 and n are constants and v(0)=v∘. At t=0,…

Q: he indicated function y(x) is a solution of the given differential equation. Use reduction of order…

A:

Q: Form the partial differential equation by eliminating arbitrary function from z=exf(x−y)z=exf(x−y)

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Q: Find general solution of differential equation. Enter transient terms if any. x^2y' + xy= 7

A: Here we will find out the required general solution for given differential equation.

Q: (y-x)y'=y-x+ 2; y=x+2√√√x+5 When y = x + 2√x + 5, Thus, in terms of x, (y-x)y' = y=x+2= Since the…

A:

Q: 11. In line integrals, if x(t) has a derivative equal to 0, with y'(t) and z' (t) not equal to 0, A.…

A: To Select: The correct the option(s): 11. In line integrals, If x(t) has a derivative equal to 0 and…

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: A normal is drawn at a point P (x, y) of a curve, it meets the x-axis at Q. If PQ is of constant…

A: We will show that the given differential equation describing such curve is correct and will find the…

Q: Particular Integral for the differential equation (D² + 25)y =(cos5x) is given by a. -xsin5x 5 b.…

A: Option; b is correct.  Given differential equation ; (D2  + 25 )y  = cos5x Let D = m; Auxiliary…

Q: 6. Use separation of variables to find product solution of u(x, y) for the partial differential…

A: Given,            ∂2u∂y2=∂u∂x+xu                        (1)

Q: 1. Find the differential equation of the family of circles of radius r whose centre lies on the…

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 7: From an integral equation corresponding to the differential equation d²y dx² dy - sin x- +exy = x…

A: What is Integral Equation: Like differential equation, there is also integral equation. In integral…

Q: Solve the partial differential differential by separation of variables 3 + 7 0. %3D

A:

Q: Example 12 : Form the partial differential equation by eliminating the arbitrary function from z= xy…

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Q: If the function f(x,y) is continuous near the point (a,b), then at least one solution of the…

A:

Q: Circles with center on the line y = x

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Q: The linear differential equation y' - cotx + 3y csc x = 0 has the integrating factor tan A tan () B…

A: The objective is to find the integrating factor of given equation: y'-cotx+3ycscx=0

Q: Find the differential equation of all family of circles with center at the line 3y - x = 0 with h…

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.