Let y = y 1 x and y = y 2 x be the solution curves the differential equation d y d x = y + 7 with initial conditions y 1 0 = 0 and y 2 0 = 1 respectively. Then the curves y = y 1 x and y = y 2 x intersect at

Step-by-step solution

We have been given that d y d x = y + 7 ⇒ d y y + 7 = d x ⇒ ln | y + 7 | = x + c ⇒ | y + 7 | = k . e x ⇒ y = k · e x - 7 ⇒ y 1 0 = 0 ⇒ k = 7 ⇒ y 1 x = 7 e x - 1 ⇒ y 2 0 = 1 ⇒ 1 = k - 7 ⇒ 8 = k ⇒ y 2 x = 8 e x - 7 ⇒ y 1 x = y 2 x ⇒ 8 e x - 7 = 7 e x - 7 Hence, No point of intersection. This is the required option.