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Let a, b ∈ R. Let y = (y_{1}, y_{2})^{T} be a solution of the system of equations
Every solution y(x) → 0 as x → ∞ if
For solving by variation of parameters. The value of Wronskion W is
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 taclocus, then
T(x, y ) is a factor of the Pdiscriminant.
III. T(x, y ) is a factor of a cdiscriminant.
IV. Cusplocus has two distinct tangent.
Choose the correct answer.
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 nonhomogeneous equation y' + p(x)y = r(x), if y_{1} and y_{2} are its solutions, then the solution of homogeneous equation y' + p(x)y = 0 is
Consider the differential equation (x + y + 1) dx + (2x + 2y + 1)dy = 0. Which of the following statement is true?
Here (x + y + 1)dx + (2x + 2y + 1)dy = 0
By separables of variables,
Integrating (2z + log z) = x + c
⇒ 2(x + y) + log (x + y) = x + c.
The orthogonal trajectory of the family x^{2}  y^{2} = C_{2} are given by
A. Singular solution contains no arbitrary constants.
B. Singular solution can be obtained from complete primitive.
Let the general solution of a differential equation be, y = ae^{bx+c} then order of the differential equation is,
If y_{1}(x) = x and y_{2}(x) = xe^{x} 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 y_{1 }and y_{2} are linearly independent solutions of the homogeneous equation L(y) =y"+p_{1}(x)y' + p_{2}(x)y = 0. Then, p_{1}(x) and p_{2}{x) are given by
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