Differential Equations Answers

Find the Wronskian of the following functions and determine whether it is linearly dependent or linearly independent on (-∞,∞).

{x2, x+1, x-3} ans, W=8, linearly independent

{3e2x, e2x} ans, W=0, linearly dependent

{x2, x3, x4} ans, W=2x^6, linearly independent

[C] Solve the following differential equation:

x^ 2 y^ " - 2xy'-4y=x^ 2 +2 log x

y''-4y'+4y=(x+1)e^x

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

A circuit has in series an electromotive force given by E=40-sin35tV, a resistor of 10Ω, and an inductor of 0.4H . If the initial current is 2 , find the current at time t>2.

Solve the following Second Order equation with constant co-efficient

y’’ - 6y’+25 y = 0.

Solve the following second order non-homogenous equation:

y" + y = sin (2x)

Solve the following Bernoulli's initial value problem differential equation:

6y’ — 2y=xy⁴ y(0)=–2

Solve the following initial value problem equation:

2x²y" + 3xy' 15y = 0, y (1)=0 y' (1) = 1

Solve the differential equation:

a) yk - y(k-1) + 2y(k-2) = k² + 5k

b) y(k+2) - 4y(k+1) + yk = 3k +2^k

In LHS yk , y(k-1) and so on is not in multiply but the k part is written in down to y( like yk is not y×k but the k is written in right down of y).

A string of length l has it's ends x=0 and x=l fixed. It is released from its rest in position y=[4 lamda x(l-x)]/l². Find an expression of the displacement of the string at any subsequent time.

Find a general solution of (4D^2+4D+17)y= 0

(2x+y-4)dx+(x-3y+12)dy=0 solve using COEFFICIENT LINEAR IN TWO VARIABLES