Let a and b be arbitrary constants and C be a fixed constant. If y=a e^ 2 x +b x e^ 2 x +C is the general solution of a differential equation, then the order of that differential equation is

Step-by-step solution

Given y=a e^ 2 x +b x e^ 2 x +c ...(i) y₁=2 a e^ 2 x +b [2 x e^ 2 x +e^ 2 x ] ...(ii) y₂=4 a e^ 2 x +b [4 x e^ 2 x +4 e^ 2 x ] ...(iii) Now eliminating arbitrary constant a, b from eqs (i), (ii) & (iii), we get the require differential equations. | array ccc y-c & -e^ 2 x & -x e^ 2 x y₁ & -2 e^ 2 x & -(2 x+1) e^ 2 x y₂ & -4 e^ 2 x & -(4 x+4) e^ 2 x array |=0 ...(iv) Since, here c is not a arbitrary constant, ' c ' is a fixed constant. Hence solving eq. (iv) will give a differential equation of second degree. aligne