X-+ Solve y(x) = Fow + by First Finding Kalkit l,FX,t, A) and Solution when FW=e2X FN = e=X

Q: a) Solve y' = 3x² + y, y(0) = 4 by choosing step length 0.1 for y(0.2) by Euler's improved method

A:

Q: particular

A: We find particular solution.

Q: ) Obtain the general solution of y" + 2y + y = e² In r

A: In this question, the concept of the differential equation is applied. Differential Equation A…

Q: 3. Obtain two linearly independent solutions valid near the origin: 3xy" +(2-x)y' - 2y = 0

A: As per the question we are given the following second order ODE : 3xy’’ + (2-x)y’ - 2y = 0 And we…

Q: Solve 1 . Find a particular solution to a' = x – y + e', y = -4x + y +t using undetermined…

A:

Q: Is y(x) = C1sin2x + C2cos2x, where C1 and C2 are arbitrary constants, a solution of y” + 4y = 0?

A:

Q: the value of lambda such that y=e^lambda*x is a solution of y''x-4y'+20=0 as: could you help me…

A:

Q: Determine the positive roots of the simultaneous nonlinear equations using the Newton-Raphson method…

A: From given non linear equation we have  f1=-x2+y-1=0f2=y-2cos(x)-1=0 iteration formula is:…

Q: When solving S3x – 2y = 5 ly = 3x – 3 by the substitution method, we obtain x = , so the solution…

A: Given equations are: 3x-2y=5......(1)y=3x-3......(2) Get the value of 3x from the equation (1)…

Q: Determine the coefficients of the equation y-ax+bx²+cx+d so that it will have critical points at…

A:

Q: x°y" – 3x'y"+ 6xy'– 6y = 0 -

A:

Q: Verify that y = h(x) =- (C is an arbitrary constant, x # 0) is a solution of xy' = -y.

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: Find a general solution of y"- iy'+6y= 0.

A:

Q: Y, = Ax² is particular solution of y' + y" = 1 for A = %3D

A: Here, yp=Ax2yp'=2Axyp''=2Ayp'''=0

Q: 6- Use Newton-Raphson method to solve the system x3 +y – 1 = 0 y3 – x + 1 = 0 with the starting…

A: f1=x3+y-1=0→(1)f2=y3-x+1=0→(2)(x0, y0)=(1, 0) Formula for Newton-Raphson…

Q: 6- Use Newton-Raphson method to solve the system x3 + y – 1 = 0 y3 – x+1 = 0 with the starting value…

A: Detailed explanation mentioned below

Q: Q2\A: By using partial method solve 2x² cos x dx

A: Given :∫2x3cosxdx

Q: Q1 : Find the solution of x, y, z by using Gramer's Rule. 3x + 2y – z = 1 x - y + 5z = -2 2x + y = 3

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

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

A:

Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 2e-2 Y(t) =

A:

Q: Obtain the particular solution. y' = x exp(y-x²) ; when x = 0 , y = 0.

A:

Q: Find a particular solution to æ' = -x – y + e', y' = 2x + y – ešt using undetermined coefficients.

A:

Q: 5. = y – xy³e-2x у —

A:

Q: If y and y, are solutions of a non-homogenous equation y" + ay + by =c then y,-Y2 is a solution of…

A:

Q: 2 ydx = 3xdy; when x = -2, y = 1 Ans. y = (x/2)3

A: Given: 2ydx=3xdy ; x=-2, y=1   We know that; ∫1ax+bdx=1alnax+b+C

Q: b) Give a particular solution for y" – 2y' + y = et - 1+x2

A:

Q: 4. Solve Ar, = 3n2 + 4n - 1 with the initial condition r = 3. %3D

A:

Q: Find the solution of y-x =0 using separable variable method. dx

A:

Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

A: Given Cauchy-Euler differential equation is

Q: Verify that y = 1/(x+ C) is a solution to y'= -y², where C is some constant. Find the particular…

A: Given that: y=1(x+C)

Q: Solve the DE using Linear First Oder Method: y +yx = x - 3. if y(0) = 2 %3D

A: Given y'+yx=x-3   if y0=2 To find the general solution

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

A:

Q: az (b) Solve and ди by applying chain rule if z = In(x² – 2y), and x = u + v, y = e". dv

A:

Q: y +y² – 1 = 0, Yı = 1

A:

Q: Use variation of parameters to find the general solution of y′′−2y′+ 2y=(e^x)csc(x)

A:

Q: 2. Obtain the particular solution. y"-y'-6y=0; when x=0, y=2,y'=1

A:

Q: (b) Find the general solution of: = yx² - xy ax Given z = y when x=1, determine the particular…

A:

Q: a. Find that solution of y' = 2(2x-y) which passes through the point (0, 1).

A: SINCE YOU HAVE ASK MULTIPAL QUESTION, SO WE WILL ANSWRING ONLY FIRST QUESTION.

Q: 8) Use Gaussian Elimination to solve: x +3y-z = 13 - 5z = 23 (4x-y-2z = 14 Consier 2x

A:

Q: Use variation of parameters to find a particular solution of y'' - Y = 4e-x 1-e-2x Yp (x) =

A: Solution of the differential equation, By using the method of Variation of perameters

Q: X-2y+3z=11 4x+2y-3z=4 3x+3y-z=4 Solve by  Gaussian elimination

A:

Q: Use variation of parameters to find the general solution of y" – 2y' + 5y = e'.

A:

Q: 4. Verify that y=cx+e² +1 is a solution of the equation y=y'x+(y')' +1.

A:

Q: (D³ + 2D² - 5D - 8)y = 0, when x = 0, y = 0, y = 0, y" = 2

A: Given