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January 21, 2021 2:17 pm 30 pts
Let us consider the equation This equation is to be squared to rationalise it and then it can be easily seen that the greatest d'y exponent of the highest ordered derivative is two. Hence the equation is of second order and second dx2 degree. It should be noted that the determination of the degree does not require the variables x and y to be made rational and integral. When, in an ordinary or partial differential equation. Note: In an ordinary or partial differential equations when the dependent variable and its derivatives occur to the first degree only, and not as higher powers or products, the equation is called linear; otherwise it is non-linear. The coeficients of a linear equation are therefore either constants of functions of the independent variable or variables. For examples, dy+y-X, * dy (COS (sinx)y = 0 dx are ordinary linear differential equations of the second order while the equations (x+y a, y- + x(sin y) = 0 dx dx2 dx are ordinary non-linear equations of the first and second order respectively. Any relation connecting the dependent as well as the independent variables will be called the solution or primitive of the differential equation, if it reduces the differential to an identity when substituted DE The solution of the differential equation does not contain any derivative. Thus REDMI NOTE 9 Al QUAD CAMERA dy 2 y 2x is a solution of the differential equation dx
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• Rudhreswaran g
also one doubt degree does not require the variable X and y to be made rational and integral means what ? what is rational and integral
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