Differential Equations - 3 - Mathematics MCQ

If y₁(x) and y₂(x) are solutions of y" + x²y' + (1 - x)y = 0 such that

then the Wronskian W( y₁, y₂) on R is

If y₁ and y₂ are two solutions of initial value problem y" + p(x)y' + q(x)y = 0, y(x₀) = y₀, y'(x₀) = y₀ and the Wronskion W(y₁, y₂) = 0, then y₁ and y₂ are

Which of the following transformation reduce the differential equation   into the form 

The general solution for  is

  in the domain R : |x| < 5, |y| < 3 the equation has

For IVP
y’ = 2y^1/2, y(0) = 0
Which one is correct in a nbd of 0?

If e^-x, xe^-x are solutions of y" + ay' + by = 0, then

The degree of differential equation satisfying the relation 

The process of formation of the differential equation is given in the wrong order, select the correct option from below given options. 
1) Eliminate the arbitrary constants. 
2) Differential equation which involves x, y, dy / dx
3) Differentiating the given equation w.r.t x as many times as the number of arbitrary constants. 

The singular solution of the differential equation p³ + px - y = 0 is

Which of the following relations hold true? 

Solving by variation of parameter for the equation y" + y = sec x, the value of Wronskion is

The eigen values for the boundary value problem x" + λx = 0; x(0) = 0, x(π) + x'(π) = 0 satisfy

Suppose y_p(x) = x cos 2(x) is a particular solution of y" + αy = - 4 sin (2x)
Then, the constant α equals

All real solutions of the differential equation y" + 2ay' + by = cos x (where a and b are real constants) are periodic if

Integrating factor of (x⁷y² + 3y)dx + (3x⁸y - x)dy = 0 is x^myⁿ, then