NCERT Solutions for Class 12 Mathematics Chapter 9 Differential Equations

Short Note:

• The order of a differential equation is the order of the highest derivative present, while the degree is the power of that highest order derivative, once the equation is free of radicals and fractions involving derivatives.

• A general solution contains arbitrary constants equal in number to the order of the differential equation, while a particular solution is obtained by assigning specific values to these constants using given conditions.

Short Note:

• In a variable separable differential equation of the form dy/dx = f(x)g(y), the variables can be separated onto opposite sides of the equation and integrated independently.

• A homogeneous differential equation, where dy/dx is a function of y/x alone, is solved using the substitution y = vx, which converts it into a variable separable form in v and x.

Short Note:

• A first order linear differential equation has the standard form dy/dx + Py = Q, where P and Q are functions of x (or constants).

• Such equations are solved by first finding the integrating factor (I.F.) = e^(∫P dx), multiplying throughout by it, and then integrating both sides.