Let a, b ∈ R. Let y = (y1, y2)T be a solution of the system of equations
Every solution y(x) → 0 as x → ∞ if
The solution of exists for all
For solving by variation of parameters. The value of Wronskion W is
The initial value problem
Consider the following statements
I. A singular solution of differential equation satisfies the differential equation but is not a particular solution of the equation.
II. If T(x, y) = 0 is the equation of the tac-locus, then
T(x, y ) is a factor of the P-discriminant.
III. T(x, y ) is a factor of a c-discriminant.
IV. Cusp-locus has two distinct tangent.
Choose the correct answer.
The general solution
where andy(0) = 0 is
Which of the following pair of function are linear independent
Select the correct code
Singular solution of differential equation contains
I. arbitrary constant
II. can be obtained from general
III. do not contain arbitrary constant
IV. cannot be obtained from general solution
For non-homogeneous equation y' + p(x)y = r(x), if y1 and y2 are its solutions, then the solution of homogeneous equation y' + p(x)y = 0 is
The solution of represents
Solve for 0 < y < 10 and y (0) = 0
The orthogonal trajectory of the family x2 - y2 = C2 are given by
A. Singular solution contains no arbitrary constants.
B. Singular solution can be obtained from complete primitive.
The solution of the differential equation sin x = 0, y(0) = 0 exists in the open interval (-a, a) then ‘a’ equals to
If y1(x) = x and y2(x) = xex are two linearly independent solutions of then the interval on which they form a fundam ental set of solution is
Using the method of variation of parameters for the particular solution to the differential equation
The general solution of the system of differential equation and M a 2 x 2 matrix
and a 2 x 1 constant vector b =
is given by
For the ordinary differential equation
which of the following statement is true?
If 2x(1 - y ) = K and g(x, y) = L are orthogonal families of curves where K and L constants, then g(x, y) is
If y1 and y2 are linearly independent solutions of the homogeneous equation L(y) =y"+p1(x)y' + p2(x)y = 0. Then, p1(x) and p2{x) are given by
Doc | 5 Pages
Doc | 5 Pages
Video | 09:50 min
Doc | 41 Pages
Test | 20 questions | 60 min
Test | 20 questions | 60 min
Test | 20 questions | 60 min
Test | 20 questions | 60 min
Test | 20 questions | 60 min