Differential Equations Answers

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)

Q. Choose the correct answer.
Q. Which of the following is the solution of differential equation du/dx=x^2/(1-u^2 )
i) x3+u3-3u=2
ii) 3/2x3+3/2u3-9/2u=3

iii) -2x3-2u3+6u=4
a. i) only
b. ii) only
c. iii) only
d. i), ii) amd iii)

Q. Choose the correct answer
Q. Which of the following differential equation (with dependent variable y) are linear
(i) (x+y)dy=x2dx+y2dy
(ii) (x2+y)dy=x2dx+ydy
(iii)(x2+y)dy=sin ydx