Request to solve the second order differential equation by range Range kutta 4th order method 8d^2y/dx^2-x^2+2y^2=0...

Request to solve the second order differential equation by range Range kutta 4th order method 8d^2y/dx^2-x^2+2y^2=0 with initial conditions y(0)=1 and dy/dx(0)=0 compute y at 1 (Numerical Method)

Expert Solution

Colby Messinger answered 1 year ago

Solve this differential equation (4x - 2y)dx + (2x - 9y)dy = 0

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x =...

Consider the following second-order ODE: (d^2 y)/(dx^2 )+2 dy/dx+2y=0 from x = 0 to x = 1.6 with y(0) = -1 and dy/dx(0) = 0.2. Solve with Euler’s explicit method using h = 0.4. Plot the x-y curve according to your solution.

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...

5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...

Solve the differential equation 2x^2y"-x(x-1)y'-y = 0 using the Frobenius Method

(10 marks) Solve the second-order linear differential equation y′′ − 2y′ − 3y = −32e−x using...

Solve the second-order linear differential equation y′′ − 2y′ − 3y = −32e−x using the method of variation of parameters.

Find the general solution of the differential equation (x + 2y) (dx-dy) = dx + dy.

Solve Homogeneous differential equation. Please show work (4x - 2y)dx + (2x - 9y)dy = 0

3. Consider4 the homogenous linear second order differential equation y′′ − 2y′ + y = 0...

3. Consider4 the homogenous linear second order differential equation y′′ − 2y′ + y = 0 (⋆) (a) Verify that the function y = e^x is a solution of equation (⋆) on the interval (−∞, ∞). (b) Verify that the function y = xex is a solution of equation (⋆) on the interval (−∞, ∞). (c) Verify that y = 7e^x + (5xe)^x is a solution of equation (⋆) on the interval (−∞, ∞). (d) Assume that c and d...

2. Find the general solution to the differential equation x^2y''+ y'+y = 0 using the Method...

2. Find the general solution to the differential equation x^2y''+ y'+y = 0 using the Method of Frobenius and power series techniques.

3. Solve the following differential equation x^2y’’ − 2xy’ + 5y = 0. A coil spring...

3. Solve the following differential equation x^2y’’ − 2xy’ + 5y = 0. A coil spring is suspended from the ceiling, a 16-lb weight is attached to the end of it, and the weight then comes to rest in its equilibrium position. The mass is in a medium that exerts a viscous resistance of 8 lb when the mass has a velocity of 1 ft/s. It is then pulled down 12 in. below its equilibrium position and released with an...

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