а) d³x d?x - 4x = 0 dt2 dt3 Hint: x(t) = e2t is a solution. %3D

Q: Find the general solution by solving with integrating factor method t(dy/dt) + (t+2)y=1

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Q: Solve the initial value problem. dv + sect, v(0) = 4 %3D dt 1+?

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Q: Use matrix exponential to find the solution of dx dt 16 5 3 Y, 9. Y, dt x(0) = 1, y(0) = 1

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Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: What is the integrating factor of the equation (2xy*ev + 2xy³ + y)dx + (x²y+ev – x²y² – 3x)dy = 0 A…

A: We have to choose the correct answer from the given option according to the given condition

Q: Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dB %3D 5 t y(1) = 2

A: Given: dy=3-y5-tdt+dBt y1=2 We have to apply Euler-Maruyama method as one step to solve the SDE.

Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: Q3. Find the solution of the given initial value problem d?x dx dr2 ++ x = 0, x(0) = 2, x(1) = 3 dt2…

A: Given that  The differential equation is  d^2x/dt^2+dx/dt+x=0 x(0)=2,x(1)=3  To find teh general…

Q: What is an integrating factor of the nonexact DE dy/dx = 1/(2xy) -2y 2y e^(y^2) e^(-y^2) O NA

A: We have to find

Q: Q1. Solve the IVP by finding appropriate integrating factor an (x² + y² – 5)dx – (y + xy)dx = 0,…

A: Consider the given differential equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x The solution…

Q: Show that the solution of the equation dx/dt=-x(k^2+x^2) With initial condition…

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Q: Find the general solution of dy – qy³ Py – dt by making a suitable substitution that transforms the…

A:

Q: (x – x2 – y²)dx + (y + x² + y?)dy = 0

A:

Q: Find the particular solution of the initial value problem: dy 3x2(y? + 1), dx y(0) = 1 %3D

A: We can find the answer as below.

Q: Apply the iterative formula, to compute the first three successive approximations to the solution of…

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: solve the initial value problem dy/dt=2sqrt(t), y(1)=5

A:

Q: Find the integrating factor of the D.E. of y(2y+ 4x – 2)dx – 2(x+ y)dy = 0. 3x b. e-2x d. e2x a. e…

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Q: Solve the differentfial equation by Using the method of integrating factor for e= dy 24. 2%. dz e-x

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Q: 3X An integrating factor for the DE dy + ydx = e³*dx 5 O ey O y O ex O x?

A: For a differential equation of the form, , the integrating factor is defined by .

Q: Solve the initial-value problem. dy t + 3y = t, t > 0, y(1) = 0 dt %3D

A: First I have written the given differential equation into the form of first order linear…

Q: Solve, the method of integrating factor: 1, order linear initial value prot 1) 2) 3) (t+1)y' - 2y =…

A: A differential equation of the form y'+P(x)y=Q(x) is called linear differential equation and its…

Q: Find the solution of the diffrential equation that satisfies the given initial condition. (dp)/(dt)…

A: The differential equation dPdt=2Pt,P(1)=5. We have to find the solution of this differential…

Q: Find the general solution of (a) dy = ty(1+ t²)-1/2 dt (b) fip' dt + (t + 2)y = 1

A: To find the general solutions of given differential equations

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

A:

Q: Solve the general solution using the integrating factors by inspection (x³y³+1)dx+x⁴y²dy=0

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Q: Solve following initial value problem and fınd the constant of integration C dy 2xv1 + x², y (3) =…

A:

Q: a) A vibrating spring can be modeled by the initial value problem: тx" (() 3D bx'(t) + kx(t) 3D 0 =…

A:

Q: An integrating factor of (x³y² + x)dy + (x²y³ – y)dx = 0 is (a)수 (b) (c) (d)을 2xy 2x

A: Given differential equation is x3y2+xdy+x2y3-ydx=0

Q: Solve the given initial value problem. dx/dt = 7x+y; x(0)=1  dy/dt=-6x+2y; y(0)=0 The solution is…

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Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

A:

Q: Find an implicit solution to the initial value proble dy = y? – 2y, dx y(1) = 3. -

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Q: Solve the initial value problem, xcosædr + (1- 6y) dy = 0; y (7) =0 %3D %3D

A: Given, The differential equation  xcosxdx+1-6ydy=0   ;  yπ=0 We have to solve it.

Q: (1 point) Find the solution to initial value problem d?y dy 12 + 36y = 0, y(0) = 8, y'(0) = 6 dt dt?…

A:

Q: Find the general solution of d²y x(x +2) dy + (x + 2)y(x) = x³, dx dx? given that y, (x) = x and…

A: The given differential equation is solving through the variation of parameters below.

Q: Let F(x,y) = xy – x² + y. What is the solution of the initial value problem dy = 0; y=1 & x = 0 ? ду…

A:

Q: Find the integrating factor of the given linear de and general solution of the…

A: Here we solve the given differential equation.

Q: Exercise 7 Find the general solution 1. 6y'dx - x(2x + y)dy = 0

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Q: (xy+2)dx+(§x*y+8x-4y* )dy =0

A:

Q: Q2: Consider the initial value problem. d²y dy y(0) = 2, dy (0) 3 a 2 0. + 2 + 6y = 0 dt2 dt

A: Since it is an homogeneous equation so complementary function is the solution

Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: H.W: Solve-Using D-operator dy dx + dt + 3y – 5x – e-t = 0 %3D dt dx dy + x + y - 3 = 0 dt dt 2.

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Q: (x³- y)dx+ xdy=0 y(1)=3

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Q: Obtain the general solution to the equation. (3t + 4y + 2)dt – dy = 0

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Q: Solve the given initial-value problem. dx = -7x – y dt dy — 9х — у dt x(1) %3D 0, у(1) 3D 1 x(t) %D…

A: Given dxdt = -7x - y      ---(1)dydt = 9x - y        ---(2)with x(1) = 0, y(1) = 1

Q: Q3: Consider the initial value problem. dy d²y dy dt? + 0.25y = 0 dt (0) = b. dt y(0) = 2, %3D %3D…

A:

Q: Find the solution to initial value problem d²y di? dy 14 + 49y = 0, y(0) = 1, y'(0) = 4 dt

A:

Q: An integrating factor of (xy? – x?) dx + (3x?y² + x?y – 2x³ + y?)dy = 0 is A) ey B) ебу 1 C) 6y e D)…

A:

Q: Solve the initial value problem. dzy = 1-e 2t, y(1) = -1, y'(1) = 3 dt? %3D

A: we have got the differential equation  y''=1-e2t , y(1)=-1,y'(1)=3 to find the value of y we will…

Q: Obtain the solution using Integrating Factors Found by Formulas 1. 2(2y² + 5xy – 2y + 4)dx +x(2x +…

A: First we making exact differential equation then find solution.

Q: Solve the given initial-value problem dr At = 3x + y – e", r(0) = 3, dt %3D dy 2x + 4y, y(0) = -4.…

A: Step:-1 Given system of differential equation is dxdt=3x+y-e4t,   x(0)=3dydt=2x+4y,   y(0)=-4 Take…

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.