Recent content by madahmad1

thx a lot mark but one last favor, can u please show me how u checked using the product rule?

the product rule states (f.g)` = f`.g + f.g` so is it? (y+2x)+ (x^2)

For 31 i re-arranged and got dy/dx= ((x^2)y +xy-y)/(-(x^2)y +2x^2). from here (x^2)/y cancel out. and I`m left with xy-y(dx)= 2x^2(dy). You can then divide by x and you are left with 1/2x(dx) = y+c by integrating the y side. but that is not correct what's my mistake? I have no clue how I can...

For problem 20 I multiplied both sides by dx to get dy= e^x+y (dx) so by integrating i get y+c= integral of e^x+y (dx) Can you please show me how to integrate the right side. I am having trouble integrating e`s

For problem 8 I got dy/dx + 2xy= sinx the integrating factor here is e^x^2/2. So then I mulitply the whole equation by that. dy/dx(e^x^2/2) + 2xy(e^x^2/2)= sinx(e^x^2/2) Can you please explain to me in detail how I would integrate this, this is where I am having the most trouble.

Ok, for problem 6, I got dy/dx + 2y/x = 1/x by re-arranging and dividing by x. Since 2y/x is the coefficient then the integrating factor is the same as before x^2. multiply all sides by x^2 I get, dy/dx(x^2)+ 2xy = x, next we integrate so x^3/3+c = x^2/2 but how do I get the answer I...

is that product 2x?

divide by x to get rid of the xy`. Si it becomes y` + 2y/x= x^3

why not? Is it e^integral 2x or e^x^2/2 ?

sorry I missed that, now I multiply all that by e^2. After that, I integrate again right?

you multiply both sides by x and then move 2y to the other side.

For problem 1. I re-arranged and got y`(x) +2y = x^3. Thus, the integrating factor is e^2x, is that correct? Now, I multiply by e^2x and continue, correct? Or is this method wrong?

yes I know both are linear equations. But, can someone please give me a clear step-by-step on how to do it? I showed you what my method and answer was but couldn`t get it to be the same as the correct answer.

For problem 1 I divided by x so x^3 divided by x was x^2 but I`m not sure if that is correct. The final answer should be y= c/x^2 + x^3/5 but I do not know how that was given. Can you show me?

For 17 integrating factor is e^-3t so I re-arrange the equation and multiply it by e^-3t. I got dy/dx e^-3t - 3ye^-3t= e^2x-3t Then I integrate it, but how do you get y= ce^3x-e^2x by integration?