Give the substitution that converts the given nonlinear equation into a linear equation then solve the initial value problem. y'-2y = y², y(0) = 1 a. y(x)=3/1+ v(x) = b. y(x) = — 2 1+e-2x c. y(x) = - d. y=3 e. y² = 1 e¹[t + 1 + e] t6 +1 2t3 5t 2+5 Ct5

Q: Q3/ Solve the following equations: 1- х(2у — 3)dx + (x2 + 1)dy %3D0 dy 2- dx 4y x (у-3) 3. y' = 2xy…

A: Note that there are so many ways to write the final answer of the differential equation.

Q: a) Show that y=e*is a solution of the linear D.E y'+y=0, and y =xis a solution of the nonlinear D.E…

A: Please find solution of both parts.

Q: Q1\ solve the equation : d²y dy + 7 +12y= 1 for initial condition y(0)= 1 y(0)=2 dx2 dx

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Q: The Bernoulli equation y'+37 xy'= 34 y can be converted to one of the following linear equations: a.…

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Q: (x-2)(dy/dx) – y =(x-2)3 solve homogenous equation by linear equation method

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Q: Find the solution. (D² - 20 - 3)y = 0; when x = 0, y = 0, y'= 4 A y = e-e B y =e+e y = e y = -e

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Q: Solve simultaneously y (t) = 1 – a"(t) z' (t) = 2y (t) x(t) = -yr(t) where x (0) = 2, x' (0) = –1, y…

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Q: x²y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 3. Determine if the two solutions in Questions 1 and 2 are…

A: The general form of a second-order homogenous linear differential equation is given by…

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Q: Solve y + y = 2y = 0, where y (0) - = 3 and y (0 y(t) =

A: y''+y'-2y=0 Auxiliary eqaution m2+m-2=0

Q: y=3 is an equilibrium solution for the d.e. y'-y=3 Select one: True O False

A: We have to check

Q: Solve for a linear equation? P(t)y'' + Q(t)y' + R(t)y = S(t)

A: We have to solve for a linear equationPty''+Q(t)y'+R(t)y=S(t)

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Q: Find a constant solution of y′ = t2y - 5t2.

A: we have to find a constant solution of  y'=t2y-5t2

Q: Eliminate the arbitrary constant. 2x y=c₁' e B A y"-y'- 2x=0 C -X (D) +c_e 2 y"-y'-2y=0 2y"-y'-2x =…

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Q: Find the solution to y - x +t y' = y if æ(0) = 1 and y(0) = 4. a(t) : help (formulas) y(t) = 8, help…

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Q: Show that a linear equation dy a(x)- + b(x)y = c(x) d.x %3D is exact if a' (x) = b(x).

A: Given linear differential equation axdydx+bxy=cx.....1 We have to show that the given differential…

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Q: (a) y" – 4y" + y' + 6y 0. (b) y" – y" + 2y' = 0.

A: General solution for the Homogeneous differential equations with constant coefficients

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: ) Solve the equation (IVP) (1 +x²) – x(1+ 2y)y' = 0 y(1) = 0 %3D

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Q: What is the equilibrium solution of the equation y '(t) = 2y - 4? Is itstable or unstable?

A: The equation given is y't=2y-4. To find the equilibrium solution of the equation y't=2y-4.…

Q: Consider the equation y' + 5y = 2. Show that the function o given by: %3D 2 $(x) is a solution,…

A: Given y'+5y=2 We have to find ∅x

Q: Find the solution. y' = y - xy³ e-2x A e2=x²(y²+c) B e2Y =x²(y²+c) (c) edx =y²(x²+c) (D D e=y²(x²+c)

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Q: Find the equilibrium solutions and determine which are stable and which are unstable. y' = 9y – 3y?…

A: According to the given information, it is required to determine the equilibrium solutions and…

Q: Find the solution. (D3 - 3D - 2)y =0; when x =0, y=0, y' = 9, y" = 0. A y = (-1+ 2x)e-2*+ e 2x B y =…

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Q: у 7. y' +²√y = 0, y(1) = 0 - x

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Q: (x - y)y' - 2y + 3x + == 0 ; y(1) = 5 + X² = 0 X

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Q: Find the solution of y' = (1 – 4x) y², y (0) = –1 in explicit form

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Q: y (4) + 32y"+256y = 0 y(0) = 2, y'(0) = 0, y"(0) = -16, y""(0) = 128

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