The value of C+D is equal to

0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

- 8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

10

No worries! We‘ve got your back. Try BYJU‘S free classes today!

8

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D $8$
$m^{3} - 9 m^{2} + 23 m - 15 = 0 \Rightarrow (m - 1) (m - 3) (m - 5) = 0 \Rightarrow m_{1} = 1, m_{2} = 3, m_{3} = 5$
we get
$y = c_{1} e^{x} + c_{2} e^{3 x} + c_{3} e^{5 x}$ ...(1)
Differentiating w.r.t x
$y^{'} = c_{1} e^{x} + 3 c_{2} e^{3 x} + 5 c_{3} e^{5 x}$ ...(2)
Subtracting (1) from (2), we get
$y^{'} - y = 2 c_{2} e^{3 x} + 4 c_{3} e^{5 x}$ ...(3)
Again differentiating w.r.t. x
$y " - y^{'} = 6 c_{2} e^{3 x} + 20 c_{3} e^{5 x}$ ...(4)
From (3) and (4)
$y " - 4 y^{'} + 3 y = 8 c_{3} e^{5 x}$ ...(5)
Differentiating is w.r.t. x we get
$y^{'''} - 4 y " + 3 y^{'} = 40 c_{3} e^{5 x}$ ...(6)
From (5) and (6), we get
$\frac{d^{3} y}{d x^{3}} - 9 \frac{d^{2} y}{d x^{3}} + 23 \frac{d y}{d x} - 15 y = 0$
$C + D = 23 - 15 = 8$

Suggest Corrections

Similar questions

The value of $10 \sum r = 0$ $c o s^{3}$ $\frac{π r}{3}$ is equal to

2 π \int 0 \frac{x {sin}^{8} x}{{sin}^{8} x + {cos}^{8} x} d x

The positive value of K for which the equation x² + kx + 64 = 0 has equal roots is :

Question 8

The value of y for which the expressions (y - 15) and (2y + 1) become equal is

(a) 0

(b) 16

(d) - 16

{log}_{10} 8

Join BYJU'S Learning Program