Q 01: solve the homogeneous ODE for given initial conditions y" – 6y" + 11y' – 6y = 0 : y(x) = 0. y'(n) = 0, y"(1) = 1 Answer:

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

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Q: Solve Differential Es: 1. 5y" + 6y' + y =0 2.9y" - 12y' + 4y =0 3. y" + 4y =0 Sin qx) ax Use: y = C₁…

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Q: The question is in the picture below.

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Q: y' = y tan x – y² sec x

A: a. The given problem is                        y'=ytanx-y2secx ; x∈0,π2

Q: 1. Find the function y(t) satisfying y' = ev-t(1+t?) sec y with y(0) = 0.

A: Claim: solution for with y(0)=0. Integrating both sides we get, Take u=e-y then du=-e-y  and…

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: The solution is given as

Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

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Q: y′ = −y(5 − y)

A: Recall the following fact.

Q: (t+2)y"-y'-(4t+10)y=0 Given y1=e-2t Find y2?

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Q: Which of the following functions is a solution of x²y" + 5xy' -21y = 0. (а) у(х) — sinx (b) y(x) =…

A: here option c is true

Q: Solve y(t) – [ (1+u)y(t – u)du = 1~ sinh t

A: Consider the given:…

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Verify that y = c is (1+ce') (1– ce') is a solution to y' = + (v² – 1) , where some constant.

A: For verifying given thing, we find solution of given differential equation Now, for finding solution…

Q: Use variation of parameters to find a particular solution, given the solutions y₁, y2 of the…

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Q: (a) (2e – x)y' = 1.

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Q: Identify f(x) to be used in variation of parameters to solve for y, e" y" + y' – 3y = x

A: To find f(x) write equation in form of y" + P y' +Q y = f(x).

Q: Find a function y=P(t)that is a solution of y'=.02y with initial condition y=100 when t=0.

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Q: tY"(t) + (1 – 2t)Y'(t) – 2 Y(t) = 0, Y(0) = 1, Y'(0) = 2 %3D

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Q: x² + y² Use Improved Euler's Method to approximate y(2) for y' = Use h=0.2. Calculate up to 4…

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Q: IL Higher Order Derivatives 3. y=2 Solve for y, y"and y" 4. y = (x + 3)i Solve for y and y"

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Q: Solve this ODE by Heun's Method and h = 0.1 to find y(0.2) y' = -3x ,y(0) = 0 0.04 O 50 1 50 3 50 1.

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Q: Solve: x" -x+ 5 y'=t y" - 4y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Approximate y'(1.6) in the function y'= 5x-2y when y(0) = 1.5, x(0) = 0.4 and the stepsize is 0.2…

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Q: Solve: x"-x+ 5 y'=t y" - 4 y-2 x' = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

A: Solution:

Q: Is the equation separable, linear, bernoulli, or homogenous? x4 + 4xy2 2x3 + x²y +y³ а. dx = x* +…

A:

Q: Solve: x" -x+ 5 y'=t y" - 4 y-2x = -2 with x(0) = y(0) = x'(0) = y'(0) = 0 Let L{x(t)} = U(s) &…

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Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" -…

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Q: Find for x = 1, the value of the particular solution y of the following ODE: 4 y"-4y'-3 y=0,…

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Q: Fill in the blank The equilibrium solution(s) of y' = 3y(1–where k > 0 are %3D he difference y',…

A: Equilibrium solutions for a differential equation are given by  y'=0 Also wronskian of two solutions…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.