Q3. Solve the equation: z* + (1 + i)z² + i = 0.

Q: Q2\ Solve the following 2y + 3y' – 2y = te-2t y(0)=0 and y'(0)=-2

A: Please see the explanation below

Q: (D² +4)y = 4cos x

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Q: Solve x?y" – 2ry' + 2y = x³ In x by first finding the complementary solution and then using the…

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Q: Q6. Find general solution of the DE 4x²y" + 8xy' + y = 0

A: This is Cauchy- Euler equation. We can solve this equation as follows :

Q: 4. Obtain the general solution. y"-4y'+4 y=3e²*

A: for the solution we have equation y" - 4y' + 4y = 3e2x so now characteristic equation of this is...…

Q: Q5) solve using crammer's rule ? x y and 1 -1 13 2 y o 3. 2 -6 -4 1

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Q: 5olve The simultaneaus.equation 22 tiw - 2 2+ (1ti)w =3;

A: Given :                    2z + i ω = 2 .................(1)2 + (1+i)ω = 3i ..............(2)then we…

Q: Solve the particular solution (D2+3D+5)y = 5e-xsin2x using  D- operator method.

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Q: Q6. Find the general solution using variation of parameters of y" + 4y = 8tant

A: We have to find the general solution of the given differential equation. For this, we will consider…

Q: solve the DE y'' - 5y' + 6y = 32xe2x, y(0) = 1, y'(0) = 0

A: *Concept:- the give differential equation is Linear differential equation of higher order with…

Q: Q1. Verify that y= is a solution of the DE -20t y + 20y = 24 %3D

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Q: Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x…

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Q: Solve the second-order equation xy" + 2y' 8x? by making the substitution u -y'.

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Q: Find the general solution to t?y" - 13ty' + 49y = 0

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Q: ェ'は) = -t I()

A: Given, First order differential equation I't =-t2It

Q: Use undetermined coefficients to find the particular solution to y''−4y=2e^−3t

A: Use undetermined coefficients to find the particular solution toy''−4y=2e^−3t

Q: (4D* – 4D³ – 23D² +12D+ 36)y = 0

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Q: 5. Solve, using the method of undetermined coefficients: y" + 2y' = 2x + 5 – e-2= %3D

A: First we shall get particular solution of y''+2y'=2x+5. Using method of undetermined coefficients y…

Q: dP/dt = P - P2 ; solve by seperation of variables.

A: It is required to solve the given differential equation using separation of variables. dPdt=P−P2

Q: dy y/5y² – 3

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Q: y' = x3 – 2xy %3D

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Q: Find all the solutions of 211 + 1z10 + 1²zº + .+1" = 0 ... to Hint: What happens when you multiply…

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Q: Q3. Solve for t ex* e2x+1 = et

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Q: 2.ryy' = y? - 2x. Find the solution that passes through the point (1,2).

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Q: Q6- By using Direct metheds solve the lineair algebric Equatione- 15 X + 3 y + 27 = 85 X - 2 y + 82=…

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Q: Solve the IVP y' = [, y+,yc0) = [2]. [et y + -1 3.

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Q: Solve the diffrential equation:

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Q: Solve the equation -2x – by – 5z = 0. = S + t

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Q: Solve the equation 2x² – 3y² = 6 for y. Is y a func- tion of x?

A: Given equation is 2x2-3y2=6. To solve for y and  to determine whether y is function of x. Solution:…

Q: Solve the equation: å oy = Esimpt t ezt-X %3D

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Q: Q3: Solve the D.E_XỲ+Y=. XY+Y= 7/2/2 y2

A: The given differential equation is  XY'+Y=1/Y2

Q: Solve y" - 5y' + 6, using characteristic equation.

A: Given differential equation is y'' - 5y' + 6

Q: Q6. Find general solution of the DE 4x²y" + 8ry' + y = 0

A: We need to find the general solution of the given differential equation. The general solution of the…

Q: Solve the nonhomogeneous equation: (D2-4)y = 2 –8x, when x=0, y=0, y’=5, using undetermined…

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Q: Solve y"-xy' - By = 0, x>0 A) y = e+ B) y = c,x* + C) y= + D) y =c,3r*+

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Q: R: Given the IBvp の o<xcL Solve for 4(XE).

A: Using separation of variables and superposition principle

Q: Find the equation for the general solution y²= cx

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Q: How many solutions does the equation ||2x – 3| – m| = m have if m > 0?

A: Modulus function is also known as absolute value function. It is represented by |x| where x is any…

Q: Q.4 Use the method of separation of variables to solve 2.xyU, +2U, = 0, U(x,0) = 3e %3D

A: Standard quasi linear  partial differential equation is given as: p∂u∂x+q∂u∂y=r  Lagrange method for…

Q: 3. Solve, showing details: y₁ = 4y2 + 5et y2 -V1-20e-t yı(0) = 1, y2(0) = 0

A: Sol

Q: 1. Solve for y. D B 420 C0y-4 8. Find MZBCD. 40

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Q: Obtain the general solution. (D^3 - 4D)y = 0 when x = 0, y = 0, y' = 0, y'' = 2

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Q: Solve the difference equation A?yn + 3Ayn – 4y, = n² with the initial conditions yo = 0, yn = 2. %3D

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Q: solve the sysyem  5x-y+2z=3 4x+5y+7z=26 x+y+4z=3 The solution is, (type an ordered triple)

A: Given equations:                               5x-y+2z=3       ....... (1) 4x+5y+7z=26…

Q: Q2/ Show that y =e2x + e-3x is the solution to the y"+ y' - 6y = 0

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Q: Solve the DE with general solution m''-3m'+2m=0

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Q: approximate with accuracy 10^3 to the solution of x³+x-4 = 0, lying in the interval [1,4].

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Q: 3. Solve, showing details: y₁ = 4y2 + 5e² y2 = -₁- 20e-t Y2 y1(0) = 1, y2(0) = 0

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Q: Q13. Use Variation of Parameters to solve the DE e2x y" – 4y : - %3|

A: