Given the differential equation dy 8x dx y Separate the Variables, and then rewrite using Integration Signs. 8x dx B dy = 8x dx 3 dx (D y = 8x dx © Su- E 8x dy = dx (F dy = 8x dx y (G dy 8x dx

Q: Given the differential equation dy 4x - y dx Split the Exponential Apart, then Separate the…

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Q: Given the differential equation cos x = y sin x, then dy dx 24. y = In (sec x) + K B Iny =In(secx)+K…

A: Here we will solve the differential equation.  Here we will use the integration  formula of tanx.…

Q: dy 4cos(2r) and y=- 2 when x=- dx 3x Suppose What is the particular solution to the given…

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Q: 2. Solve the given differential equation by separation of variables. (e' I l}°e * da 1 (e* | 1 dy =…

A: 1) Given ey+12e-y dx + ex+13e-x dy = 0ey+12e-y dx  = -ex+13e-x dyex dx(ex+1)3 = -ey dy(ey+1)2∫ex…

Q: Given, ( +) dx + ( y4 Aæ+1) dy = 0 is an exact differential equation. %3D Determine the value of A.

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Q: Given the differential equation dy e4x + y dx Split the Exponential Apart, then Separate the…

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Q: dy = xe with y(0) = 4 dx

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Q: Is (1+ex/y)dx + ex/y(1-x/y)dy = 0, a exact differential equation? If yes then, find the value of y.

A: Exact differential equation- A differential equation of the type Mdx+Ndy=0 is said to be exact if,…

Q: dy If the differential equation dx is solved via the substitution z = u-, the resulting equation is…

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Q: Evaluate the given differential equation. dy 4sin2x dx y = 2; x 2

A: To evaluate: The differential equation dydx=4sin2x. Given: The condition for the given differential…

Q: The value of the constant a such that the given differential equation is exact ) 1 1 dx + 1 dy = 0…

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Q: (x2 + y2 - 5)dx = (y+ xy)dy, y(0) = 1 %3D

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Q: et the differential equation. xy'dy = (y³ – x³)dx Highlight the result of substitution, result of…

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Q: Evaluate the given differential equation (3siny – 5x)dx + 2x°coty dy = 0

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Q: Given the differential equation dy 1 +y y %3D dx i. State whether the differential equation above is…

A: A separable differential equation is any equation that can be written in the form y' = f(x) g(y).

Q: Given the differential equation dy 5x cos(y) dx Separate the Variables, and then rewrite using…

A: Topic = Differential equation Correct option = D

Q: In the differential equation (xy+1)dx+x(x+4y-2)dy=0, the integrating factor is,

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Q: Show that the particular solution of the differential equation d'y dx? dy -3 +2y = 20 sin2x dx is y…

A: We have to solve

Q: Consider the differential equation dy/dt = y−y2. Given that y(0)=0.5, solve the differential…

A: To find the expression for y(t) and find the limit y(t) as t tends to infinity

Q: The integrating factor of the non-exact differential equation (r*y + y°)dx – (3° + x*y)dy = 0. is 1…

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Q: Find the Particular integral for the given differential equation d²y dy -8 + 15y = cos5x dx2 dx (10…

A: d2ydx2-8dydx+15y=cos5x

Q: Given the differential equation dy 3x dx Separate the Variables, and then rewrite using Integration…

A: Given the differential equation is dydx = 3xy3

Q: 1 dy Q.1 Show that the function y = is a solution of the differential equation = 1- dx

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Q: Show that xy = ae" +be* +x is a solution of the differential equation. d'y +2- -x+x-2=0. X dx

A: If we differentiate   the given  solution equation two times  and  get  the given differential…

Q: Match the differential equation dy / dx = sin 2x with its slope field.

A: Match the differential equation dy / dx = sin 2x with its slope field.

Q: Consider the differential equation x². dx? d'y dy --y 0. Which of the dx following is a solution to…

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Q: Which of the following differential equation can be solved using separation variables? a. (x-2y)dx +…

A: Topic:- differential equations

Q: The differential equation (3x²e" – 2x}dx + (x*e' -sin y}dy = 0 is exact because ƏN ƏM Qu20[>_30imh…

A: Topic:- differential equations

Q: Solve the fourth order differential equation completely d*y d°(y/x) dx sin(x)+ cos(x) %3D 3 dx³

A: Given: A fourth order differential equation…

Q: Find the Particular integral for the given differential equation d'y dy -8- dx dx + 15y cos5x

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Q: An appropriate substitution for the differential equation =y(xy³ – 1) is: dx is: x = u y y = u oとー…

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Q: Given the differential equation dy 5xy dx Separate the Variables, and then rewrite using Integration…

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Q: Find the differential equation by eliminating arbitrary constants "A" and "B" from the family of…

A: Formation of differential equation: As a rule, one requires n+1 relations to eliminate n quantities.…

Q: Given the differential equation dy 1 X · = -+ y dx y i. State whether the differential equation…

A: For (i), A first order separable ODE has the form of Ny·y'=Mxxdydx=1y+ySubstitute dydx with y' ⇒xy'…

Q: Solve the separable differential equation dy 11x – 4yyx? +1 0. dx Subject to the initial condition:…

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

A: Given a differential equation, d2ydx2+y=x+sin8x;dydx=1 & y=0 When x=π To find the solution of…

Q: Find the general solution of the separable differential equation. xy dx+ sqrt(xy) dy = 0

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Q: . Solve the differential equation dx 8 7. + di? 1, L are constants subject to the conditions, where…

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Q: Find all values of r for which y = ert solves the differential equation dy dy - 12 + 20y = 0- dt dt2

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Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: d y dy Find the solution of the differential equation 2- dx +4y = 10 sin 2x with to the initial 4 dx…

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Q: Find the equation which satisfies the separable differential equation dy – 14x dx with the initial…

A: We will find out the required solution for given differential equation.

Q: Which of the following differential equation can be solved using separation of variables? a.…

A: Topic:- differential equations

Q: Determine whether the given differential equation is exact. Show the solution. (xy+ x²)dx − dy = 0

A: To determine:           If the given equation is exact or not=?   So,      The given equation is:…

Q: Solve the given differential equation by separation of variables. dx y In(x) dy y + 1\2 %3D

A: Given : yln(x) dx/dy = ( y+1 / x )2

Q: dx + 2- + x = u(t) x(0) = x'(0) = 1 dt %3D %3D dt

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Q: Which of the following is the general solution to the differential equation dx %3D 2 (3х + у)2 — 1?…

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Q: Find the differential equation y(x – 1)dx – (x² – 2x – 2y)dy = 0 a.x² + 2x + 4 = 2Cy² b.x² + 2x + 4y…

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Q: Given the differential equation (ye-* - sin x) dx – (e ¬*+ 2y) dy =0, what is the value of f'(y)? (A…

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