Question

1
Which of the following is the general
solution to d2y/dx2 + 3dy/ dx - 10y =
0?
In each case, A and B are arbitrary
constants *​

Answer 1

Answer:

1hekfijsglpiouttewwgjuy24

Answer 2

SOLUTION

TO DETERMINE

The general Solution of the differential equation

$\displaystyle \sf{ \frac{ {d}^{2}y }{d {x}^{2} } + 3 \frac{dy}{dx} - 10y = 0 }$

EVALUATION

Here the given differential equation is

$\displaystyle \sf{ \frac{ {d}^{2}y }{d {x}^{2} } + 3 \frac{dy}{dx} - 10y = 0 }$

$\sf{Let \: \: y = {e}^{mx} \: \: be \: the \: trial \: Solution }$

Then the auxiliary equation is

$\sf{ {m}^{2} + 3m - 10 = 0}$

$\sf{ \implies \: {m}^{2} + (5 - 2)m - 10 = 0}$

$\sf{ \implies \: {m}^{2} + 5m - 2m- 10 = 0}$

$\sf{ \implies \: m(m + 5) - 2(m + 5)= 0}$

$\sf{ \implies \: (m + 5) (m - 2)= 0}$

$\sf{ \implies \:m = - 5 \: , \: 2}$

So the required general Solution is

$\sf{y =A {e}^{ - 5x} + B {e}^{2x} }$

Where A & B are are arbitrary constants

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