Answers to selected odd-numbered problems begin on page ANS-2. dy dy 2ty(y – 1) dt + y? = ty dt 19. P 20. 3(1 + t²) an In Problems 21 and 22 solve the given initial-value problem. dy 2ху %3 Зу, у(1) %3D} 21. x dx dy + y3/2 = 1, y(0) = 4 dx 22. y/2 Each DE in Problems 23–30 is of the form given in (5). In Problems 23–28 solve the given differential equation by using an appropriate substitution. dy dy 24. dx 1 — х — у (x + y + 1)² 23. x + y dx dy dy 26. dx tan?(x + y) sin (x + y) 25. dx dy dy 28. dx 2 + Vy – 2x + 3 1 + ev-x+5 27. dx In Problems 29 and 30 solve the given initial-value problem. dy 29. dx cos (x + y), y(0) = 7/4 Зх + 2y dy 30. dx y(-1) = –1 Зх + 2у + 2" Discussion Problems 31. Explain why it is always possible to express any homogeneous differential equation M(x, y) dx + N(x, y) dy = 0 in the form dy F dx an х You might start by proving that М'x, у) %— х"М(1, у/x) N(x, y) = xªN(1, y/x). and 32. Put the homogeneous differential equation (5x2 — 2у?) dx — хуdy %3D 0 into the form given in Problem 31. copied, scanned, or duplicated, in whole or in part. WCN 02-200-202

Q: Find the particular solution for initial value problem.

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Q: 4. (a) Show that the solution of the initial value problem y = 1+y. y(0) = 0 is y(r) = tan z.

A: y'=1+y2 Given to show that this initial value problem on solving gives y=tanx

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A: Given initial value problem can be evaluated as shown below by using substitution method

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Q: Find an explicit solution of the given initial-value problem. x20Y = y - xy, y(-1) = -2 dx y =

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Q: (a) Use the fact that 5x? - y? = c is a one-parameter family of solutions of the differential…

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Q: Show that y = C1e^2x + C2e^-x is a solution of the differential equation y"- y'-2y = 0. Also, find a…

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Q: Solve the initial value problem 8(t+1)dy/dt−7y=7t, for t>-1 with y(0)=19. y=

A: Differrntial equation problem

Q: 2. Solve the initial value-problem: . dY dt Y with Y(0) = (1,0). - 4

A: The solution is given as

Q: 5) For the initial value problem y'(t) = y + ty, y(0) = 1, use Euler's method with time step At =…

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Q: 3. Consider the initial value problem (IVP): ty' — y = t²e-t, y(1) = −1. (a) Use integrating factor…

A: We will use integrating factor method to solve this.

Q: 6. Verify that y(x) = /E+ 9 is a solution of the initial-value dy problem 1 and y(0) = 3. 2y dx ||

A: To verifyy(x)=x+9 is  a solution of the given IVP dydx=12y

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Q: Solve the Initial Value Problem. (1 – 3t)– dy - у %3D 0, у(2) %3D —4 dt

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A: SOLUTION-

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Q: (2) Consider the following system of differential equation, with time domain t e (0, 1): a' = -2x +…

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Q: 5(a) Using Adam-Moulton predictor-corrector method, find the solution dy - = y-ť, y(0) =1 at t = 1.0…

A: Note: As per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Solve the initial-value problem y" + 4y" + 5y' + 2y = 10 cos t, y(0) = 0, y'(0) = 0, y"(0) = 3.

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.