Solve the ODE

Show how you would have done things by hand. Find the solution to the attached ODE.

Four Problems about an ODE

Show how you would have done things by hand. Consider the differential equation attached. The graph is shown. a) Is this differential equation linear or nonlinear? Is it autonomous or nonautonomous? b) Without solving, use the graph to determine the limiting value... (see attached for rest).

ODE: Variation of Parameters

Please see the attached file for the fully formatted problems. One solution of the equation attached is y(t) = t. Find the general solution. Use variation of parameters to find a particular solution of the equation attached.

Continuous Functions, Fundamental Set of Solutions and Coefficient Functions

Consider the attached differential equation where I = (a,b) and p,q are continuous functions on I. (a) Prove that if y1 and y2 both have a maximum at the same point in I, then they can not be a fundamental set of solutions for the attached equation. (b) Let I = {see attachment}. Is {cos t, cos 2t} a fundamental set of solu ...continues

Kirchoff's Laws : Mass-Spring Equation

Consider a basic electric circuit with a resistor, capacitor, and inductor and input voltage V(t). It follows Kirchoff's Laws that the charge on the capacitor Q = Q(t) solves the differential equation: {see attachment}, where L (inductance), R (resistance), and C (capacitance) are positive constants (depending on material). The ...continues

System of Equations : Matrix Form, Eigenvalues and Phase Portraits

Consider the attached system of equations. (a) Write the system in the given matrix form {see attachment} (b) Determine the eigenvalues of A in terms of the parameter {see attachment} (c) The qualitative nature of solutions depends on .... (d) Sketch a typical phase portrait... **Please see attachment for complete set o ...continues

Equivalent Systems : Second Order to First Order Equations

Write the given second order equation as its equivalent system of first order equations {see attachment for details}

Equivalent Systems : Second Order to First Order

Write the given second order equation as its equivalent system of first order equations {see attachment for details}

Equivalent Systems : Second Order to First Order (Velocity Function)

Write the given second order equation as its equivalent system of first order equations {see attachment for details}

Eigenvalues of Matrix

Calculate the eigenvalues of this matrix: {see attachment} Note: You'll probably want to use a graphing calculator to estimate the roots of the polynomial which defines the eigenvalues.