The number of arbitrary constants in the particular solution of a differential equation of third order are: (A) 3    (B) 2     (C) 1     (D) 0

The number of arbitrary constants in the general solution of a differential equationof fourth order are:(A) 0 (B) 2 (C) 3 (D) 4

Assertion: The general solution of ( dy ) /( dx) + y =1 is y e^x = e ^(X)+C Reason: The number of arbitrary constant in the general solution of the differential equation is equal to the order of D.E.

if a, b are arbitrary constants, find the differential equation of y=acosnx+bsinnx

Statement 1 : Order of a differential equation represents the number of arbitrary constants in the general solution. Statement 2 : Degree of a differential equation represents the number of family of curves. Which of the following Statement is/are are correct ?

Find the particular solution of the differential equation: (1+e^2x)dy+(1+y^2)e^xdx=0 , given that y(0)=1

If a is arbitrary constant, find the differential equation of x^2+y^2=a^2

Which of the following statements on ordinary differential equations is/are true ? (i) The number of arbitrary constants is same as the degree of the differential equation. (ii) A linear differential equation can contain products of the dependent variable and its derivatives. (iii) A particular integral cannot contains arbitrary constants. (iv) By putting v=(y)/(x) any homogeneous first order differential equation transforms to variable separable form.

If a and b are arbitrary constants, then the order and degree of the differential equation of the family of curves ax^(2)+by^(2)=2 respectively are

If A and B are arbitrary constants, then find the differential equation corresponding to the equation y=Ax+B .

Verify that the function y=C_1e^(a x)cosb x+C_2e^(ax)sinb x ,\ C_1, C_2,\ are arbitrary constants is a solution of the differential equation (d^2y)/(dx^2)-2a(dy)/(dx)+(a^2+b^2)y=0