5

4. [1.6] Find the general solution of the DE: (r_y)y'= 2xy Answer: y= C(x? +y)5.[1.6] Find the general solution of the DE: xy'+6y = 3xy4/1 Answer: y= [(+C...

Question

4. [1.6] Find the general solution of the DE: (r_y)y'= 2xy Answer: y= C(x? +y)5.[1.6] Find the general solution of the DE: xy'+6y = 3xy4/1 Answer: y= [(+Cx)'

4. [1.6] Find the general solution of the DE: (r_y)y'= 2xy Answer: y= C(x? +y) 5.[1.6] Find the general solution of the DE: xy'+6y = 3xy4/1 Answer: y= [(+Cx)'



Answers

In Problems $7-16,$ obtain the general solution to the equation.
$$ \frac{d y}{d x}=x^{2} e^{-4 x}-4 y $$

We want to solve eight. Y minus two equals four. Why? Plus 16? All right, let's get the wise to the same side Souls attract for why? And I end up with four. Y minus two equals 16. Next, I want this for y to be alone. So let's add to and I end up with four y equals 18 since four is multiplied by why I will undo by division divide out of four and then we'll simplify that. So 18 4th is the same as nine halfs. And of course I want to check that. My answer really works. So I will plug that right in here. Eight times nine halfs minus two. Is that equal to four times nine halfs plus 16. Okay, two goes into 84 times. So this is 36 minus two. Two goes into four twice. So this is 18 plus 16 and 36. Minus two is 34. 18 plus 16 is 34. Check why equals nine. House

If I don't mind most wine otherwise you, you the journalist Visa Art. Why you are square post P r. Yeah. To us. We're hero cars right here, Teoh.

In this problem, we need to. So the question why Squire over y plus four equal to 16 overs y plus four. So let's let us just multiply both sides. Multiplayer both size mitt y plus four you will be getting Why squad over? Why, plus four into why plus 4 to 16 over. Why plus four. Two y plus four. This will get cancelled out. So we are having we will be having who I square recalled to. I said, not being hit Good. Now, right now. So I was quite equal to 16 which means why call toe plus minus under 16 which means where called a plus minus For So we have two solutions where called Minus four and why I call to soar No, if me observe discreetly carefully If a why plus four become zero The whole expressing becomes undefined So why less? Four cannot be called a zero, So why cannot be equal to minus four? So why call to minus four will be neglected? We have only why apple toe full as answer. Thank you

Hello. We have to solve the growing dependency allocation that is 16 D to the power four by minus by close to zero. So I was education Well we 16 empty the bar for Man is very close to zero. So forward, I mean squared Man is one is good because 20 so for EMC squared minus one multiplied with food and square Has money close to zero. So we can add it to where -1 to M plus one into four M squared plus one cost +20 So roads will be M and when is one way to M two is -1 x two & M three will be oh Plus -1 were 12 ι.. Okay here Alfa Syrian be days when we do so the solution of the differential a question ken readiness solution can readiness very close to she went into the power of Monex plus E to E to the power of M two X. Bliss into the powerful fags for this complex rules. The solution is eating well, facts plus C. three Shen with tax Plus c. four Cosby tax mm. So this will be closed to why will be closed to see one right into the power eman you do about amber. That is heck. So I do plus you do. Your department is X. Y. two Alpha zero. So this believe one. Okay, so C three said X. Y. To place C. Four, Of Course X. Y two. So this is the solution for the given differential equation. I hope you understood.


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