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.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

Solve the following pDEs
A). d²u÷dx²= 8xy²+1
B). d²u÷dxy- du÷dx=6xe^x

The area bounded by a curve, the x-axis, a fixed ordinate, and a variable ordinate is proportional to the difference between the ordinates. Find the equation of the curve.

Solve the below differential equation
y'''+3y''+2y'-5y=sin2t