In Problems 37 through 42, determine by inspection at least |one solution of the given differential equation. That is, use your knowledge of derivatives to make an intelligent guess. Then test your hypothesis. 37. y" = 0 39. xy' + y = 3x² 41. y' + y = e* 38. y' = y 40. (y')² + y² = 1 42. y" + y = 0

Q: What is the solution of the differential equation by da = a(2a' + y)dy ? a. 1. = .3 O b. 1 1 2 O . 1…

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Q: Determine whether the differential equation is linear а. х- у 3D ху 1 b. y' = y c. y' = xy? = Vx d.…

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Q: Suppose f(x, y) = x" + y*. Find fa(1, 1), f,(1, 1), and fz (x, y)

A: Given :f(x,y)=xy+yx

Q: Show the process in solving this differential equation

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Q: 5. Find the solution of the differential equation y =- xy + xy³ (Bernoulli)

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Q: Give the degree of the following differential equation  y' - y^2 + y^{(3)} =0

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Q: 3. Solve the differential equation y' - 2ty = t by multiplying both sides by an appropriate…

A: Given differential equation:-    y' - 2ty = t

Q: How many parameters are there in the differential equation * у 3а сos bх + c sin bx+4 а. 2 b. 3 С. 4…

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Q: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

Q: Solve the differential equation with appropriate method. Finalize answer equated to y. y' = 2xy - x

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Q: An infectious disease is spreading at rate proportional to the number of people with the disease, or…

A: Given C= initial value= 118  For t=8, P=358 We have to find k

Q: Solve the given differential equation. 16х?у" + 16ху' -у %3D0 y(x) = ,x > 0

A: CAUCHY EULER differential equation

Q: What is the solution of the following differential equation that satisfies y (1) = 7 and y '(2) = 3?…

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Q: (Зу' + 48у)x3 + Зу'x? — 27ух %3D 0

A: Given differential equations To determine the general solution

Q: Find the general solution of the differential equation 2xyy' = 2y² – x²

A: given 2xy y' = 2y' -x'y' = 2y2-x22xy---(1)put y =vxy' = v + xv'---(2)so from (!) we have y' =…

Q: y" - бу' + 9 %3 0 which of t equation? I. y = C1e3* + C2xe3*

A: Here we find the auxiliary equation.

Q: e'sin2 xdx + e2Ycosxdy= ycosxdy 1

A: Given differential equn is eysin2xdx+e2ycosxdy=ycosxdy⇒(eysin2x)dx+(e2ycosx-y…

Q: 53х dx (53x + 1)2 A) 3 V5x + 1 + C B) – 3 V5x + 1 + C In5 3 C) 3ln5 (V5x + 1) + C D) V5x + 1 + C 3…

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: Solve the given differential equation by undetermined coefficients. у"+у'- 30y %3D2х y(x) =

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Q: y"+y = cosecx cotx %3D

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Q: What is the differential equation of 2y'=3y+1 when y(1)=0

A: Consider the provided D.E 2y'=3y+1  when y1=0 We need to find the solution of the given D.E, Since,…

Q: 9. Find the general solution of the differential equation y" - 2y' = sin 4x.

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Q: у" — бу' — 7у %3D 8e7x

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Q: Show that the differential equation dy / dx = y / x is inexact and that a factor of 1 / x ^ 2 can…

A: Given differential equation is, dydx=yx.

Q: у" — бу' — 7у%3D11 sin 4x -

A: We have to mention the general form of the particular solution