Question

(b)Solve D²y + 5Dy + 6y = e-2x cos2x​

Answer 1

Answer:

Heya friend,

Here is the answer you were looking for:

\begin{gathered} {9}^{x} \times {3}^{2} ( {3}^{ \frac{x}{ - 2} } )^{ - 2} = \frac{1}{27} \\ \\ {(3}^{2} )^{x} \times {3}^{2} ( {3}^{ \frac{ - 2x}{ - 2} } ) = \frac{1}{ {3}^{3} } \\ \\ = {3}^{2x} \times {3}^{2} ( {3}^{x} ) = {3}^{ - 3} \\ \\ {3}^{ 2x } \times {3}^{2} \times {3}^{x} = {3}^{ - 3} \\ \\ {3}^{2x + 2 + x} = {3}^{ - 3} \\ \\ {3}^{3x + 2} = {3}^{ - 3} \end{gathered}

9

x

×3

2

(3

−2

x

)

−2

=

27

1

(3

2

)

x

×3

2

(3

−2

−2x

)=

3

3

1

=3

2x

×3

2

(3

x

)=3

−3

3

2x

×3

2

×3

x

=3

−3

3

2x+2+x

=3

−3

3

3x+2

=3

−3

As the bases are same, so putting the powers equal:

\begin{gathered}3x + 2 = - 3 \\ \\ 3x = - 3 - 2 \\ \\3x = - 5 \\ \\ x = - \frac{5}{3} \end{gathered}

3x+2=−3

3x=−3−2

3x=−5

x=−

3

5

If any doubt, please ask ;)