- Employ Picard's method to obtain y (0-1) of the equation ay = x +y, given that Y, =0 when x, = 0.

Q: Find the solution of the DE using variation of Parameters y''' - 3y'' + 3y = (ex/x)

A: The given problem is to find the solution of differential equation using method of variation of…

Q: Ans: (x + y)e+y = C y'+--2

A: Given differential equation is homogeneous differential equation which can be solved by converting…

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: 2y t y (1) = 1 y' = and cbtain У, , Уг and y…

A:

Q: Find the 2nd solution by reduction of order. y" - 4y + 4y=0; y₁ = e²x

A: Here given the differential equation as y''-4y'+4y=0 .......(1) And it's one solution is y1=e2x

Q: Use Euler's method to approximate the solution to y' = y + 2t , y(-1) = -1 on the interval [-1, 1]…

A:

Q: 4. xydx + (y √ x² + y²-x²) dy=0

A:

Q: Show that the function f(t) = 1² – } is a solution of the dif- ferential equation (y')² – 4y = 2.

A: Given:       f(t)=t2−12.Differential equation is: (y')2−4y=2

Q: Apply Euler-Cauchy Runge-Kutta method for the equation: and obtain y' = 29 t y (1) =1 y, y, and y. 3…

A: Hint: Formula for finding n-th approximate solution of IVP  dydx=f(x,y), y(x0)=y0  is…

Q: y(3) for y' = xe3x - 2y, y(0) = 0 by using Euller's method. h = 0.5

A: Here I write a small piece of python code to solve this problem.

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex²

A:

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

A:

Q: 4(a) Verify that the equation y = In(*/y) is an implicit solution of the IVP, %3D ydx (xy + x)dy…

A:

Q: Q1) find the critical point of the following equation - g(x, y) = x² + y² + 2xy − 6x - 3y + 4

A:

Q: 1. Apply the Trapezoid method to the ODE x' = -x + t/x for two steps with x(0) = 1 and h = 1/4. Show…

A:

Q: Find the general solution to y" – xy' = 0. -

A:

Q: Find the general solution to the equation xy” + 2y'− xy = 0 Using Frobenius.

A: xy''+2y'-xy=0 →l  Let y=∑n=0∞ cn xn+r  ⇒y''=∑n=0∞ cn(n+r)xn+r-1   ⇒y''=∑n=0∞ cn(n+r)(n+r -1)…

Q: Find a particular solution to y"+2y' + y =t

A:

Q: 1. Solve for y3 using the method of successive approximation. dy = x + y; y(1) = 1

A:

Q: A rocket travelling into orbit has a projectile given by the equation: f(x, y) = 3x3 + 2x² – 5x + 2…

A: As equation of projectile contain only x So y remain constant throughout the journey .Distance…

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

A:

Q: Find the general solution to y" – y = t e

A:

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: SOLVE THE EQUATION (y -2) dx - (x-y-Ddy = o ISSING THE DE LINEAR IN x 4 Y VAKIABLES.

A:

Q: find general solutions (for x>0) of the Euler equation x2y"+xy'+ 9y = 0

A:

Q: Find the general solution to t²y + (t + 1) y =t', for t > 0.

A:

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

A:

Q: Qe/ Salve the Euler- Cauchy equation xy'- xy+9y=o ?

A:

Q: Find general solution to Cauchy-Euler equation: (t^2)y''-2ty'-3y=t^2

A:

Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h=D 0.1) using Runge-Kutta.

A:

Q: x²dx + y(x-1)dy = 0 %3D

A: We need to find solution of differential equation.

Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: x²y" – 3ry + y = x°, r>0.

A:

Q: | (3x+-x²) dx=Ax° + Bx² +C, for Suppose that %3D constants A, B, C. What is the value of C if the…

A:

Q: 2d) Let a e R find the solution of y' (x) – ay(x) = 0

A: as you didn't mention question number to be solvedso I solved first question. For Further solution…

Q: -Find the solution of y"+y' + by = 0 by transforming y = x"u|

A: Put y=xαu in the given equation y'=xαu' y"=xαu" Then the equation becomes xαu''+axxαu'+bxαu=0 Now…

Q: 8. Using the Runge-Kutta method of the fourth, solve y" = y + xy', y(0) = 1, y'(0) = 0 to find…

A: We take y'=z the Given equation is y''=y+xz,y(0)=1,y'(0)=0,y(0.2)=?…

Q: Ql: Find y(0.5) for y'=-2x-y, y(0) = -1, with step length (h= 0.1) using Runge-Kutta.

A: Since you have asked multiple question, as per our guidelines we are supposed to answer only one…

Q: Find an actual explicit solution to y′=t/y,y(2)=−1.

A:

Q: Find the value of C2 so that the function y = Cqe2x + C2e* + 2 sin x satisfies the initial…

A: Given, The function y=c1e2x+c2ex+2sinx We have to find the value of c2 which satisfy the initial…

Q: 2. Find the general solution. y' + sec x y = cos x. а. b. y' +y =÷(e* -e-*).

A:

Q: Q1:-Using Euler method to find y (2) using h-D0.5 for y' = 9 **, y(0) 1

A: # we are entitled to solve one question at a time, please resubmit the other questions if  you wish…

Q: If f(x, y) = -x - y* + 3xy - 2x - 5y, then in the process of obtaining its critical points the…

A: Introduction: The critical points of the two variables' function f(x,y) is given by solving the two…

Q: Find the general solution of the di f ferential equation *+ x .2 d²y + (x² – )y = 0.

A:

Q: 3- Use Euler Method to find value of Y(1.6) when Y(1) = 0 for %3D (x2 + y2)dx = (x + y)dy, use h =…

A: The solution is given as

Q: Use the Runge-Kutta method to solve the equation y" = xy' +y for x= 0-0(0-2)2-0 given that at x = 0,…

A:

Q: Find a general solution to the Cauchy-Euler equation x°y'"' - 8x²y" + 9xy' – 9y = x², x> 0,

A:

Q: The singular points for the D.E. (x² – 2x– 3)y" + 4xy' + 2y= 0, are:

A:

Q: Given d'y dx² = 6x-0.5x², y(0) = 0, y(12)=0, Use step size h = 4, z1 = 20, and z2 = 25. Enter 4…

A:

Q: Find a general solution to the given equation for t<0. 1 26 y"(t) - '(t) +

A:

Q: 1) Find the general solution to the equation y(t) to 2y" + y – y = 3e-t + 2e¬t/2 Using the method of…

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

Q: Find the value(s) of m such that the function y=e^(mx)is a solution of the DE 2y"+7y'-4y=0

A: Find the value(s) of m such that the function y=e^(mx)is a solution of the DE 2y"+7y'-4y=0