Solve y" + y = F(t), in which F(t) = 1– t²/n² if 0

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A: Given:

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Q: Solve the inhomogeneous 1st order equation U₂ - U₁ = cost U(x, 0) = 0.

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Q: The system dx/dt = x + y, dy/dt = x + 2y + 1 has a constant solution. true or false?

A: dx/dt = x + y,dy/dt = x + 2y + 1

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Q: The function y =x is one the solution of (x-1)y-xy'+y= 0. we use reduction to order method, second…

A: Given y=x is one solution of x-1y''-xy'+y=0. Let, y=vx be another solution of the given equation.…

Q: Find general solution of U" + U = 0.

A: Given differentiation equation is U''+U=0. We have to find the general solution of the given…

Q: (1 point) Solve the system 1 6 dx dt -1 6 with the initial value 13 æ(0) = 6 a(t) = %3D

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Q: Suppose that y' = f(y) has no constant solutions, where f : R -> R is infinitely many times…

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Q: If f(x) = 4e e 2(e - 1) 2e ľ e²² dt, then f' (1) = 0

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Q: (17) = ² × ( ¹²7 ) = ² × x=(²7)e²+(²1) ²² = ₁₁ (²₁) e² + c₂l(¹) te² + (1) e¹ dx dt dy dt O 2x + y -X…

A: The differential equations are:And,To Do:We have to solve the system.

Q: True or False The system dx/dt = 2y dy/dt = sin(xy) has only one equilibrium point.

A: We need to equate both the derivative to 0, to calculate the equilibrium points.

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Q: Obtain two linearly independent solutions valid near x = 0 x(1-x)y" - 3y' + 2y = 0

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Q: solve  utt- 4uxx=x2          -infinity 0  subject to initial conditions: u(x,0) = x  ut(x,0)=0

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Q: Given that the three-state model equation are d[A] dt d[B] dt d[C] dt -a[A] + B[B] = = a[A] -…

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Q: Obtain two linearly independent solutions valid near x = 0  x(1 - x)y" - 3y' + 2y = 0

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