Differential Equations - 8 - Mathematics MCQ

An integrating factor of x dy/dx + (3x + 1)y = xe^–2x is

What is the reason behind the non-existence of any real function which satisfies the differential equation, (y’)² + 1 = 0? 

What is the order of the partial differential equation,

A particular integral of y" - (a + b)y' + aby = Q(x) is, 

The homogeneous differential equation M(x, y)dx, N(x, y) dy = 0 can be reduced to a differential equation, In which the variable are separated, by the substitution 

General solution of  

 is the general solution of

In linear ordinary differential equation, the dependent variable and its differential coefficients are not multiplied together and occurs only in

General solution of the equation   Given that y = sin x is a solution, is

Solve d³y/dx³ - d²y/dx² - 4dy/dx + 4y = 0 has the solution

The P.I. of the differential equation (D³ - D)y = e^x + e^-x,  is

If φ(x, y) = 0 is a singular solution, then φ(x, y) is a factor of

P.I . of 

The complementaiy function of (D⁴ - a⁴)y = 0 is

A differential equation of first order and first degree is homogeneous, if

The integrating factor for the differential equation 

Given, an equation  and a solution of it is y = a₀ + a₁ sinh x + a₂ cosh x, where a₀, a₁, a₂ are arbitrary constants, then this solution is