Rewrite the following linear equation as a system of first order equation of t y' = A(t)y + g(t): y(4) ty(3) + (sint)y" - 10y = e²t.

Q: Solve the system -1 dx dt with x (0) 2 x2 = -1 1 2 [:] 1 x Give your solution in real form. x1 = An…

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Q: dy = 2y and the solution to this equation includes the point (-1, 1), then y = dx 5. , Given (A) e²r…

A: Given : dy/dx= 2y includes point (-1, 1)

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

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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…

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

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Q: let h(y)=(y-3y2)5(y2+2)6  h'(y) in simplified form.

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Q: For z = 2-8 i, find the value of the expression exp(-5i22), and type its real part, imaginary part…

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Q: Solve this linear IVP,        xlnx dy/dx + y= 2lnx,                           y(e)=2

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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)

Q: Solve the nonlinear ODE Ay''+Byy''-y=0, where y=y(x) and A,B are constant

A: The given nonlinear ODE is: Ay"+Byy'-y=0 where y=yx and A,B are constants.

Q: Definitions. A linear operator T on a vector space V is called nilpotent if Tp= T0 for some positive…

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Q: What physical systems might the Chini equation, y*y' + f(x) = g(x)*y, represent? Can you tell me…

A: The Chini equation, given by  y∗y′+f(x)=g(x)∗y , appears in various physical and engineering…

Q: 1. Describe each of the following equations, giving its order and telling whether it is ordinary or…

A: 1)Given DE is y"+3(y')2+4y=0. We find it's order and decide whether it is ordinary or partial and…

Q: If y = v3x , then y' is A. -1/2 B. V3 x -1/2 С. /3x V3 D. 2 V3 -1/2

A: Given y=3x

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

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

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

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…

Q: If y = 2² is one solution of x²y" + 2xy' − 6y = 0, find the other linearly independent solution.

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Q: A dog is walking in a straight line on the road looking for bones. The dog is attracted to the smell…

A: The function x(t) indicates the position of dog with respect to time, t. So, the velocity of dog is…

Q: Solve the DE: (2-x) y³ +(2x-3) y'' - xy' + y = 0, x<2, given that y(x) = ex is a solution of the…

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Q: If y = x2 is one solution of x2y''+2xy'-6y=0 and the other linearly independent solution.

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Q: Solve the following equations: 1. (D-D2-2D)y = 0 2. 4Dy-13Dy + 6y = 0 3. D'y - D'y – Dy + y = 0 %3D

A: On solving ist three questions we will get

Q: Find a particular equation for the DE: y+4y'-2y= 2x -3x+6

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Q: For the system, Y'=6 –1]y Y 5 4 Write the natural period of the oscillations, round the answer to…

A: This is a question of mass-spring system, application of differential equation.

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: dy dx - 5y = xy³, -5 2 y(1)=1

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