6. xy³dx+ (y+ 1)e-*dy = 0 %3D Answer: e*(x – 1) =÷++ + C 2y2 7. dz – (4x3 – 4x°z+x°z?)dz + (4y – 1)(2 – z)²dy = 0 Answer: -+ 2y² – y = C

Q: (x² + y²)dx – xydy = 0 -

A:

Q: Solve the following initial value problem using the undetermined coefficients method: d'y dt2 + y =…

A: Given d2ydx2+y=8cos2x-4sinx with yπ2=-1,  y1π2=0

Q: (0-2) dy do With initial value problem // (0) = -1 - 2X - = 3 (8-2) seco tano

A:

Q: The homogenous D. E. with constant coefficient of at least order which has the solution y = 7x2 +…

A: Here we have to find ode of given solutions

Q: 5- The equation (y`-y =e2x ) is : ( linear, exact, separable, Bernoulli )

A:

Q: 6. Find a particular solution to the inhomogeneous equation y" – 9y' + 8y = e2* |D in the form y(x)…

A:

Q: Cons i der the linearsystem X2 1. 2. is Gauss-s eidel method

A:

Q: 1. The integrating factor of (4xy + 3y² – x)dx + x(x+2y)dy = 0. 2. The standard form of Bernoulli's…

A:

Q: Find an explicit solution of the given initial-value problem. x2dy 3D у - ху, у(-1)%3D -4 dx

A:

Q: 4: A:Find the solution of the initial value problem (d^2 y)/(dx^2 )+5 dy/dx+6y=0□( ) y(0)=2, And…

A: Given A. d2ydx2+5dydx+6y=0  ;  y0=2 and dydx=0 B. 2yz-3lnz=2x+5y

Q: Find the general solution of (xy + 4x)y = 5y² + 4xy². a) Oy + 12y- = -5 In |x| – 16x + C b) Oy - 4y-…

A: First order non linear ordinary differential equation.

Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

A:

Q: Suppose we are given y₁) and y2(x) (with y₁ ‡ y2), which are two different solutions of a…

A:

Q: the particular solution of the following nonhomogeneous D.E y''-2y'+y=4x^2+e^x     by undetermined…

A: Solve ( d^2 y(x))/( dx^2) - 2 ( dy(x))/( dx) + y(x) = e^x + 4 x^2: The general solution will be the…

Q: 1. Solve by Euler's method and by classical 4th-order RK method: dy₁ = 2y₁ - 4y2, dx dy₂ = y₁ - 3y₂…

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

Q: cos (2t + ) dt e21-3 -3 e 4 64e3 7 e-3 4 7 e3 4

A:

Q: Find the general solution of (y + 1)dx + (4x - y) dy = 0 Show your solutions on a separate sheet of…

A:

Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

A:

Q: The following are three different methods for solving y (t) = f(t, y(t)): (A) Yn+1 = Yn + ¥ [S(tn,…

A: Given : three different methods for solving y't=ft,yt : A yn+1=yn+∆t2ftn,yn+ftn+∆t, yn+∆t ftn,ynB…

Q: The method used in solving the first order Bernoulli's equation dy ay +b (x) y=c(x) y" dx where n#0,…

A: We have to find the differential equation

Q: Find general solution for y"+y'+2y=0 and state whether it is undamped, underdamped, critically…

A: in the given question first off all we have to find the genrel solution of the given differential…

Q: 91, Sove a, ychea (2ay-e3) dy- 0 b, Solve initial value problem (37'+ 9ay Sy')de - (bx'4liny) dy- 0…

A:

Q: he method used in solving the first order Bernoulli's equation +b(x) y=c(x) y where n#0, n#1 is…

A: Bernauli equation substitution

Q: number 20 on image attached

A:

Q: Question 1 Prove that 4 = ucy)e is a Solution for d24 - y°4 = 0 dy?

A: Given differential equation is d2ψdy2-y2ψ=0         (1) We have to check ψ=u(y)e-y22 is the solution…

Q: Find the general solution of the Bernoulli equation 2yy′= y^2+ t + 1.

A: To solve given differential equation first we solve for rearrange the equation in the form of first…

Q: Q1-Find dy / dx for the following functions : e0 -2 2.8ln2 Y: Cosh9x * Inxy 4 6. cos0 log2 2 Q2-…

A: By bartleby rules, only Q1 has been answered.  Given function is…

Q: Find an explicit solution of the given initial-value problem. x2 dy = y - %3D у — ху, у(-1) %3D -1…

A: Firstly we will solve the given differential equation by using variable separable form then…

Q: 3. Solve the problem y(t) – y(t) = 4t with initial condition y(0) behavior of the solution as t → o…

A:

Q: 2) Discuss the type , linearty, singulavity and homugenity d- the following equations; )) ux)=1-x+…

A: Given: (1) u'(x)=1-x+∫0xu2(t)(x-t)3dt, u(0)=2 (2) u(x)-1=∫0xcot(u(t))dt-∫-11(x-t)2u(t)dt (3)…

Q: 7. Solve the following Cauchy-Euler equation d’y dx² dy +5x- +3y = In x. dx

A:

Q: Consider the initial - value problem y' --2x, y(1)-2. Show that Taylor's method of order 2 ives the…

A:

Q: az dz 10. Compute and for the following equation. dy ,3 eY + xz2 6xy*z³ %D

A: The given equation is: ezy+xz2=6xy4z3...(1)

Q: 2. Given y' = x² + y . With y=-1 when x=0. b. Calculate y(0.4) and y(0.6) using modified Euler…

A:

Q: What is the solution to the initial value problem y" – 2y' + 10y = 0, y(0) = 3, y'(0) = 0 ? %3D A) у…

A: To find the solution to the given initial value problem.

Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y?, y(0) = 1.

A: the general form of the Bernoulli equation is dydx+P(x)y=Q(x)yn we have, y'=5.4y-12y2 rearranging it…

Q: Find general solution for y"+2y'+y=0, y(0)=1, y'(0)=-2 and state whether it is undamped,…

A: Find the general solution of the equation y’’ + 2y’ + y = 0, y(0) = 1 and y’ (0) = -2   The given…

Q: 2. Estimate the solution at z 3 for 2r-y y0) -1 using Euler's Method with a step size of h=1. (a) 1…

A:

Q: Find an explicit solution of the given initial-value problem. 2 dy dx = y - xy, y(-1) = -3 y =

A:

Q: In this problem, y = 1/(1 + c,e) is a one-parameter family of solutions of the first-ord initial…

A: Given: y=11+c1e-x, y0=-17 For finding expression of y, first we find value of c1 Now, for finding…

Q: (1 – xy)-2 dx + [y² + x²(1 – xy)¯2] dy = 0; when x = 4, y = 1.

A:

Q: 3. Find the solution of the initial-value problem d'y_3dy +2y=e* dx y(0)=1, y'(0) = 0 dx Using…

A:

Q: The solution of (1 +y²) + (t – elan-lyay dt 0 is: Select one: a. t = ce2tan-ly+2 O b. -C elan-ly…

A:

Q: 3. Find the general solution of the Bernoulli's Equation. y = 5.4y – 12y, y(0) = 1. %3D

A:

Q: Find an explicit solution of the given initial-value problem. dy y (2) = 2 %3D dx x2-1

A: An equation which involves the derivative or differential coefficient is called differential…