Differential Equations Answers

solve(d^2+dd'-6d'^2)z=cos(2x+y)

Show by the method of variation of parameters that the general solution of the differential equation -y^''=f(x) can be written in the form y = φ ( x) = c₁+c₂x-∫₀^x(x-s)f(s)ds where c₁ and c₂ are arbitrary constants.

Find the Fourier Sine and Cosine transformations of the following function f (x) =2 if x< 0<a and f(x)=0 if x>a

Solve the following initial value problem

1. U_t(x,t)=10U_xx(x,t) -1<x<1, t>0
2. U(-1,t)=U(1,t) U_x(-1,t)=U_x(1,t) t>0
3. U_x(x,0)=x+1 -1<x<1

Find the general solution of following

1) y''-2y'+y=e^xsin^-1(x)

Consider ABC an equilateral triangle of sides 4cm.

(a) determine the position of the center of gravity of the equilateral triangle

(b) determine and construct the set of points C such that IMA + MB + MCII = 12/√3

(c) name the set of points C

The conic F is defined as 9x²-36x+4y² = 0

a) State the nature of F

b)Determine its characteristic elements

c) Sketch F

Study the following functions

5) f(x) = I2x - 3Ie^-1/x

The gradient of the tangent to a curve is given by dy/dx = y / x(x+1). The point P(3,6) lies on the curve.

a) Find the equation of the tangent to the curve at P.

b) Solve the differential equation to find the equation of the curve in the form y=f(x).

The gradient of the tangent to a curve is given by dy/dx = x²+1 / y², y ≠0. The point P(-1,1) lies on the curve .

a)Find the equationof tangent to the cuve at P.

b) Solve the differential equation to find the equation of the curve in the form y= f(x).