Differential Equations Answers

1/xy² +y4 is an integrating factor for the differential equation (x²y + y²)dx + (y³ - x³)dy = 0

x1/

Find the general solutions of the following system

1. dx/dt = -4x+2y , dy/dt = 5x/2 + 2y

2. X' = ( -1 3

- 3 5) X

3. X' = ( 4 -5

5 -4)X

Differentiate with respect to the variable

(1) y=5/x^4 find dy/dx

(2) y=sin3t, find dy/dt

(3) 11sin4t - 5cos5t, find dv/dt

(all workings out)

Using the method of undetermined coefficients, find the general solution of the differential equation y^(iv) -2y^''' +y^''=3 e^-x+2 e^x x + e^-x sin (x ) 

y=sin3t find dy/dt

v=11sin4t - 5cos5t, find dv/dt

differentiate with respect to x

y=12e^5x

y=ln3x

(D3 − 3D2 − 6D + 8)y = xe−3x

A bike is accelerating in yz-plane with its speed given by ()

at

t(w2) +2 * u2: dvt)

at

= u2

= u3 * t(2+w3)+3*u3, subject to the initial conditions,

v,(0) = n2; v0) = n3. Determine its speed at later time

u2 = 4 + 0.3R, u3 = 2+ 0.4R, w2 = 0.5+ R,w3 = 1+ R, n2 = 3.1+ 0.2R, n3 = 4.1 + 0.1R, p1 = 5.4 + 0.2R

Solve the boundary value problem

y^''(x)+(2/x)y^'(x) - 4y(x) = -2 , 0<x<=1

y^'(0)=0, y(1) = 5.5

by using cubic spline approximation.

Solve the Bessel's equation of order zero

y^''(x)+(1/x)y^'(x)+y(x)=0

With boundary conditions y^'(0)=0, y(1)=1

Solve the following non-homogeneous linear ODE of first order

dy/dx + 3y/x =6x^2