Linear Differential equation

A differential equation of the form dy/dx+Py=Q is said to be a linear differential equation. Integrating factor of this differential equation is e^(intPdx) and its solution is given by y.e^(int Pdx)=int (Qe^(int Pdx))dx+c . Answer the question:Solution of differential equation (1+y^2)dx+(x-e^(-tan^-1y)dy=0 is (A) y=tan^-1x+c (B) ye^(tan^-1x)=tan^-1x+c (C) xe^(tan^-1y)=tan^-1y+c (D) none of these

Statement-1: The solution of differential equation (1+x^2) dy/dx+2xy=4x^2 is 3y(1+x^2)=4x^3+c .Statement-2: The solution of a linear differential equation can be obtained by multiplying it by its integrating factor. (A) Both 1 and 2 are true and 2 is the correct explanation of 1 (B) Both 1 and 2 are true and 2 is not correct explanation of 1 (C) 1 is true but 2 is false (D) 1 is false but 2 is true

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.

Obtain the differential equation of linear simple harmonic motion.

Homogeneous differential equation || reducible to homogeneous differential equation linear

which one of the following differential equation is not linear ?

Determine the order and degree of each of the following differential equation.State also whether they are linear or non-linear: ((dy)/(dx))^(2)+(1)/(dy/dx)=2

Determine the order and degree of each of the following differential equation.State also whether they are linear or non-linear: (dy)/(dx)+e^(y)=0

Determine the order and degree of each of the following differential equation.State also whether they are linear or non-linear: (y')^(2)+(y')^(3)+s in y=0

Differential Equation - Solution Of Differential Equation|Variable Separable Differential Equation - Type 2|Questions|Type 3 - Exact Differential|Questions|Homogeneous D.E.|Linear D.E.|Questions|Type 2 - Bernoulli D.E|Questions|OMR