Question

14. Solution of the differential equation p2-8p+15
(A) p=5,p=3
(B) (y-5x-c)(y-3x-c)=0
(C) both A and B true
(D) all of these​

Answer 1

(B) (y-5x-c) (y-3x-c) =0 is the correct ans

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

Solution of the differential equation

$\sf{ {p}^{2} - 8p + 15 = 0}$

(A) p=5,p=3

(B) (y-5x-c)(y-3x-c)=0

(C) both A and B true

(D) all of these

EVALUATION

Here the given differential equation is

$\sf{ {p}^{2} - 8p + 15 = 0}$

Then the auxiliary equation is

$\sf{ {m}^{2} - 8m + 15 = 0}$

$\sf{ \implies {m}^{2} - (5 + 3)m + 15 = 0}$

$\sf{ \implies {m}^{2} - 5m - 3m + 15 = 0}$

$\sf{ \implies m(m - 5) - 3(m - 5) = 0}$

$\sf{ \implies (m - 3) (m - 5) = 0}$

$\sf{ \implies \: m = 3 \:, \: 5}$

Hence the required solution is (y-5x-c)(y-3x-c)=0

FINAL ANSWER

Hence the correct option is

(B) (y-5x-c)(y-3x-c)=0

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

1. M+N(dy/dx)=0 where M and N are function of

(A) x only

(B) y only

(C) constant

(D) all of these

https://brainly.in/question/38173299

2. This type of equation is of the form dy/dx=f1(x,y)/f2(x,y)

(A) variable seprable

(B) homogeneous

(C) exact

(D) none ...

https://brainly.in/question/38173619