Question

Find the value of a so that the differential equation y ' − xy − 6x = 0 has a solution of the form y(x) = a + bex2/2 for any constant
b.

Answer 1

Answer:

a = -6

Step-by-step explanation:

Answer 2

Hello,

$y=a+be^\frac{ x^{2} }{2} \\\\ y'=a'+b*x*e^\frac{ x^{2} }{2} \\\\ y'-xy-6x=0\\\\ a'+b*x*e^\frac{ x^{2} }{2}-b*x*e^\frac{ x^{2} }{2}-ax-6x=0\\\\ a'=x(a+6)\\\\ \dfrac{a'}{a+6} =x\\\\ ln (a+6)= \dfrac{x^2}{2} +c\\\\ a=k*e^\frac{ x^{2} }{2}-6$