using the method of variation of parameters solve the following d2ydx2 y tan x 71012

Name: using the method of variation of parameters solve the following d2ydx2 y tan x 71012
Uploaded: 2022-06-02T19:55:20-08:00
Duration: 9 min 32 s
Channel: Shafiq Rehman
Description: using the method of variation of parameters solve the following d2ydx2 y tan x 71012

Step 1: Write the given differential equation in the form (y'' + y = tan(x)).

Using the method of variation of parameters solve the...

Transcript

00:01 Hello students here is a question that we have to use the method of variation of parameters to solve this equation we can write it as d square y plus y is equal to 10 x now we can take y common from here and do we have d plus 1 into y is equal to 10 x okay now we will write our auxiliary our auxiliary equation is d squared plus 1 is equal to 0 into y is equal to 0 so from here d squared plus 1 will be equal to 0 and d square will be equal to minus 1 and d will be equal to plus minus iata so it's a complex number for a complex number we know that the c f equation will be equals to c1 cos x plus c2 sign x now here we know that from here we can say that y1 is equals to cause x y2 is equals to sine x and w is equals to 10 x we will use the formula our formula is that that okay now this is what we get from our see if now we will find the we will use the ronkney's determinant to find w so by using ron skin determinant and w is equal to y1 so we know that y1 is cos x y2 is sine x y because the differential of cause is equals to minus sine x and the differential of sine x is cause x from here cause times cause is cause square and minus into sine square into sine square minus minus will be plus from here we will get co square x cost square x and the time sign is sine square and minus minus will be plus sine square x and we know that co -square x plus sine square x is equals to 1 now we know that the pi will be equals to minus y integral of y 2 x x upon w dx plus y2 integral of y1 x upon w it's capital d x now we will put the values in this equation and we will solve it to get your answer and it will be because we know that y1 is cos so minus cos x integral of sine x and here we have we know that x is equals to here x is equal to 10x and w is equal to 1 so x so 10x divided by w will be 10x dx plus y2 is a sine sine integral of y1 is cause x and x divided by w x is 10x and w is one so that's why we cannot we can if we here we have 10 x now minus cos x integral of sine x we know that we can write 10x as sine x upon cos x and here we have dx plus sine x integral of cox and 10x 10x will be equal to sine x upon cause x d x now minus cause x integral of sine x squared divided by cause x dx plus sine x integral of cause and cause will be cancelled and here we have sine x d x okay now we know that sine square x it will be equal to you know right cose x integral of sine square x will equals to co square x minus 1 sorry minus co square x plus 1 divided by cos x dx plus sine x integral of sine x d x is minus cos x now in minus cause x integral we can write cause x separately with both of these and if we write it with cosquare x here we get minus cause x plus and one upon cause will be equals to second x dx plus plus minus minus minus cause x sine x so we apply integral separately with both of these and we get minus cause x into integral of cause x here we have minus dx plus integral of second x dx minus cos x sine x.

07:27 Okay, here we have cause x minus cox...

Question

Using the method of variation of parameters solve the following. d2y/dx2+ y = tan x.

Question

Using the method of variation of parameters solve the following. d2y/dx2+ y = tan x.

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