Differential Equations Answers

Use the method of variation of parameters to solve the differential equation:

y"-2y'+y=xe^xtan-1x

Solve the following differential equation by using the method of undetermined

coefficients:

𝑦"+4𝑦=3𝑥+𝑐𝑜𝑠(2𝑥)

[D] y''-25y=0; y1=e^5x the indicated function y1(x) is a solution of the given differential eqution.Use reduction of order or formula as instructed, to find a second solution y2(x).

The lines of electric force of two opposite charges of the same strength at (-1,0) and (1,0) are the circles through (-1,0) and (1,0). Show that these circles are given by x^2 + (y - c)^2 = 1 + c^2. Show that the equipotential lines (which are orthogonal trajectories of those circles) are the circles given by (x + c*)^2 + y^2 = c*^2 - 1.

Let the electric equipotential lines (curves of constant potential) between two concentric cylinders with the z-axis in space be given by u(x,y) = x^2:+:y^2 = c (these are circular cylinders in xyz-space). Using the method in the text, find their orthogonal trajectories (the curves of electric force).

Solve this Diffrential equation (1-x^2)y"-2xy'+n(n+1)y=0 using Power Series Method

F or the follow ing differential equation locate and classify its singular points on the x-axis

𝑥²𝑦′′+ (2−𝑥)𝑦′= 0.

Find a power series solution of 𝑥𝑦′=𝑦

1) dx/dy+4y=12 for y(0)=1 (general nad particular solution)

Find the solution of (3x-y+6)dx +(6x-2y-6)dy=0 using Case 1