Q1:- Solve the following DEs:- 5) y' = 2x-2y+1 x-y

Q: O Solve y' = x + y + xy, y(0) = 1 by choosing step length 0.2 for y(0.4) by Euler's modified ethod

A: Given y'=x+y+xy, y(0)=1 Take f(x,y)=x+y+xy, Using the euler formula, Since it is given that h=0.2.…

Q: Q2\ Solve by picard method (up to four approximation) y' + y = e* and y(0)=0 Find y(0.1)?

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Q: ty (t+1)y + y = t²

A: Given That : ty"-(t+1)y'+y=t2 To find: solve the differential equation using determinant coefficient…

Q: Q7. Solve the Cauchy-Euler equation (i) 4.x²y" + 4.xy' – y = 0. (ii) 4x²y" + y = 0.

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

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Q: 4ry" +2y' +y = 0. Solve using Frobenius

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Q: Use variation of parameters to find a general solution: y(3) – 4y = et.

A: Given differential equation: y3-4y'=et         ...(1)

Q: Q.1 Solve the IVP: y" + 3y' + 2y = 686(t) with conditions: y(0) = 0, y'(0) = -1.

A: The given initial value problem given is y"+3y'+2y=6δ6t       with conditions y0=0, y'0=-1…

Q: the solution of the homogenous equation (хусот х -)dy - Ydx = o

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Q: Solve IVP using the Euler's substitution: 4 ÿ' = [_† !]ÿ, y' y(0) = [²]. Solve using the method of…

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Q: Q1. (4 marks) Find the general solution of the Cauchy-Euler equation: ry - 3ry + y = , 1>0.

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Q: 4. (D² + 2D + 5)y = 4e-*cos²x

A: Given differential equation is: d2ydx2+2dydx+5y=4e-xcos2x Auxiliary equation corresponding to given…

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method *

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Q: Determine exact solutions for the equation 2sin2x-3sinx + 1 = 0 in the interval x e [T, 3n].

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

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Q: 6z dy (78)a

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Q: t with y(0) Solve y + 5y ing %3D 4 express- the particular solution as a convolution.

A: In this question, we have to find the particular solution of the differential equation by help of…

Q: Find the General solution Use method of undetermined coefficients. 1. (D² l)y=ex (2sinx + 4cosx).…

A: To Find: the general solution using the method of undetermined coefficients   1. D2-1y=e-x2 sin(x)+4…

Q: Use the Adam-Bashforth method of the second order to solve the second equation y’=y(x+y) when h=0.1…

A: Given differential equation is y'=y(x+y), step size h=0.1 with initial condition y(0)=1 Let x0=0,…

Q: Solve the DE x²y"+xy'+ (x²-÷) y=x³/2, given that Yı=x-1/2sinx and y2=x-1/2cosx are two solutions of…

A: Given the given DE is x2y"+xy'+x2-14y=x32. y1=x-12sinxy2=x-12cosx

Q: y" + 2y' = 121?

A: To find the general solution of a given non homogeneous differential equation first we will find…

Q: Solve for all possible solution in the equation y^2 + y = x + Inx + e^y - x^2, using Secant Method

A: We have the following equation in two variables : y2 + y = x + ln(x) + ey - x2   As there are two…

Q: Use the method of Variation of Parameters to solve. SHOW WORK. y" – y' – 2y = 2e-t

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Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: y" – 2y' + y = –3 – x + x²,

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Q: Find the solution of y" – by' + 9y = 16 et with y(0) = 2 and y' (0) = 1.

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Q: Find the general solution and particular solution of this equation. (Non-anonymous question) xydx +…

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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: 4 Solve y" – y" – y' + y = 2e¬t + te' + 3 by using both the method of undetermined coefficients and…

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

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Q: Use an appropriate substitution to solve the equation z15 and find the solution that satisfies y(1)…

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Q: 2. Solve the diophantine equation x = y'.

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

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Q: 1. y' + 2y = x²y³ .2.3

A: Given problem:- solve the given differential equation y' +2y=x2 y3

Q: he equation ay"+ by' + cy = 0 has a unique solution satisfying y(0) = 1 and y'(1) = 2.

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Q: Use variation of parameters to find yp of x²y" - 2xy' + 2 y = -12 x(1/2) given that yi = x and y2 x2…

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Q: y" + 2y" + y" = x + eX %3D

A: Given the differential equation y'''' + 2y''' + y'' = x + ex We find the particular solution form…

Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

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Q: Solve of the following equation 4 y' +y = x'y? Given by x3 In x – c -x3 In x + c O Option 1 O Option…

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Q: solve the following non-linear equation with secant method xex - cosx = 0

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

A: Given Cauchy-Euler differential equation is

Q: 42. y" + 4y = sec² 2x

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Q: Solve by making the appropriate substitution

A: Given equation

Q: 1. y' = x3 – 2xy, when x = 1 and y = 1

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Q: 2. Determine the general solution of y(") = x- 2y cot (2x)

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Q: Use variation of parameters to obtain the general solution. y''+4y = 4 sec2x

A: The given differential equation is; y"+4y=4sec2x.

Q: Find the general solution of y"+25y=sec(5x)

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