Question

solve
(D^2+1)y=secx​

Answer 1

Step-by-step explanation:

How to solve your problem

(

2

+

1

)

⋅

(d^{2}+1) \cdot y

(d2+1)⋅y

Simplify

1

Distribute

(

2

+

1

)

⋅

{\color{#c92786}{(d^{2}+1) \cdot y}}

(d2+1)⋅y

2

+

1

{\color{#c92786}{yd^{2}+1y}}

yd2+1y

2

Multiply by 1

Solution

2

+

Answer 2

Answer:

The partial differential equation (D^2 + 1)y = sec(x) gives y = (c1 + c2) × cos(x) + i × (c1 - c2) × sin(x).

Step-by-step explanation:

To solve the partial differential equation (D^2 + 1)y = sec(x), where D represents the differential operator, we can use the method of characteristic equations.

First, we find the characteristic equation by setting (D^2 + 1) = 0, which gives us two roots:

D = ±i

Next, we write the general solution as a linear combination of exponential functions with these roots:

y = c1 × e^(ix) + c2 × e^(-ix)

where c1 and c2 are arbitrary constants.

Finally, we use the fact that sec(x) = 1/cos(x) to obtain:

y = (c1 + c2) × cos(x) + i × (c1 - c2) × sin(x)

The solution can then be written in terms of real functions:

y = real_part(y) + i × imag_part(y)

where real_part(y) = (c1 + c2) × cos(x)

and imag_part(y) = (c1 - c2) × sin(x).

Note that the above solution is only valid for real values of x. To find the values of the constants c1 and c2, we would need to use additional information or boundary conditions.

To learn more about partial differential equations, click on the link below:

https://brainly.in/question/50633293

To learn more about exponential functions, click on the link below:

https://brainly.in/question/17685582

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