DIFFERENTIAL EQUATION

Question

Task №1

Find the general and particle solutions of the following differential equation

a.    differential equation of the first order with the separable variables

-4x • y' + 5y=0, y=1,x=1

b.   Linear homogeneous differential equation of the second order with the constant coefficients

y'' - 13y' + 3y = 0

Task №2

 

Find the general and particle solutions of the following differential equation

a.    differential equation of the first order with the separable variables

4 • 2^y • y' + 5 =0, y=0, x=0

b.   Linear homogeneous differential equation of the second order with the constant coefficients

y''- y' +16y =0

Answer 1

Task #1

A.

-4xdy/dx=-5y

Integral -5y dy = integral -4x dx

(-5y^2)/2=-2x^2+C

Y^2=(4x^2+C)/5

Y=sqrt((4x^2-2C)/5)

Solving for “c” using y=1 and x=1

C=-1/2

Therefore:

Y(x)=sqrt((4x^2+1)/5)

B.

char.  equation

r^2-13r+3=0

r= 13/2+/- sqrt (157)/2

y(x)=Ae^(12.76x) +Be^(0.235x)

A and B are unknown constant.

Task #2

A.   This is a nonlinear ODE???

B.    Char. Equation

r^2-r+16=0

r=1/2+/-3.96i

y(x)=e^(.5x)(Acos(3.96x)+Bsin(3.96x))