Differential Equations Answers

Kindly assist me solving the following questions
1. (x^2y^2+xy)ydx + (x^2y^2-1)xdy=0
2. (x^2+y^2)dx + xdy=0
3. dy/dx +y=3y^3e^x

Solve the heat conduction equation:
for the following boundary and initial conditions:
8(d^2u/dt^2)=(du/dt), for 0<X< 5 and t> 0,
u(0,t) = u(5,t) = 0,
u(x,0) =2sin(πx)− 4sin(2πx)

Q. Choose the correct answer.
Q. The equation u_xx 〖-4u〗_xy=0 is
)parabolic
b)hyperbolic
c)Elliptic
d) None of above

Q. The equation u_xx 〖-4u〗_xy+ 4uyy=0 ?
)parabolic
b)hyperbolic
c)Elliptic
d) None of above

Q.Choose the correct answer.
If one of the solution of the differential equation (x-1)u’’-xu’+u=0, x>1 is
U=ex, then which of the following is the second linearly independent solution?
a)u=xex
b) u=3ex
c)u=x
d)u=x2+1

Q.Choose the correct answer.
Q. The equation u_xx 〖-4u〗_xy=0 is
)parabolic
b)hyperbolic
c)Elliptic
d) None of above

Q.Choose the correct answer.
Q. For what value of r all solutions of the equation
u^''-(2r-1)u^'+r(r-1)u=0 tend to zero as x→∞?
a)r=1
b)r<0
c)r>0
d)r<1

Q.Choose the correct answer.
Q. The initial value value problem dy/dx=|y|1/2 ,y(0)=0 has:
a) unique solution
b) No solution
c) Infinitely many solution
d) Two solutions.

Q.Choose the correct answer.
Q. The initial value value problem dy/dx=|y|1/2 ,y(0)=0 has:
a) unique solution
b) No solution
c) Infinitely many solution
d) Two solutions.

Q.Which of the following equations is homogenous
i) (x2+3xy+y2)dx+x2dy=0
ii) dy/dx=(x^2 (x-y)(x+y))/(x^4+y^4 )
iii) dy/dx=((x-y+1)(x+y+1))/(x^2+y^2 )
a. i) only
b. i) and ii)
c. ii) and iii)
d. i) and iii)