3 MATHEMATICS Example 1 Find the order and degree, if defined, of each of the following differential equations (i) cos 0 dy x dx −= (ii) 2 2 2 0 d y dy dy xy x y dx dx dx −= (iii) y ye′′′ =2 y′ 0 Solution (i) The highest order derivative present in the differential equation isVerify that x^2 cy^2 = 1 is an implicit solution to \frac {dy} {dx} = \frac {xy} {x^2 1} If you're assuming the solution is defined and differentiable for x=0, then one necessarily has y (0)=0 In this case, one can easily identify two trivial solutions, y=x and y=x If you're assuming the solution is defined andLn sqrt (x^2 y^2) 1/2 ln (x)^2 arctan (x^2 y^2)/x^2 ln (x) C = 0 and ln (k) {sqrt (x^2 y^2)} ar Continue Reading dy/dx = (y x)/ (y x) (1) Let y = xv then dy/dx = x (dv/dx) v Substitute in (1), you get x (dv/dx) v = (xv x)/ (xv x) = (v 1)/ (v 1) Thus
Find The General Solution Of Differential Equation X 2 Yx 2 Dy Y 2 Xy 2 Dx 0 Sarthaks Econnect Largest Online Education Community
