6.) THE FUNCTION IS A SOLUTION TO THE DE. Proving: Let C1+C3=C4 then, y=C4e^x + C2e^(2x) y'=C4e^x + 2C2e^(2x)= y+C2e^(2x) y''=C4e^x + 4C2e^(2x)= y+3C2e^(2x) y'''=C4e^x + 8C2e^(2x)= y+7C2e^(2x) Substituting, y'''-6y''+11y'-6y=0 [y+7C2e^(2x)]-6[y+3C2e^(2x)]+11[y+C2e^(2x)]-6y=0 y+7C2e^(2x)-6y-18C2e^(2x)+11y+11C2e^(2x)-6y=0 [y-6y+11y-6y]+(7-18+11)[C2e^(2x)]=0 0y+0[C2e^(2x)]=0 0=0 Therefore, the given function is a solution to the differential equation.
This is informative! Hats off to you, Sir! I am a HUMSS grad, currently taking an engineering program kaya medyo nahirapan ako sa Calc. Btw, pwede po malaman kung saan po ang source or book po neto, for review na din po. TIA. I subscribed!
Pwede po ba sa ex no.2 na I transpose yung negative sa right side para equal din sila sa left? Kahit hindi 0=0 ang answer? Ans: 4c1cos2x+4c2sin2x = 4c1cos2x+4c2sin2x
Super comprehensive ng mga video niyo, Engr! Currently cramming for an admission exam and your videos are saving me 😭😭😭 thank you so much, engr!
You can do it! You're very much welcome!
Sa assignment it is a SOLUTION po hehehe, thank you Engineer
You're welcome engr!
Thank you po sa mga vids nyo po Engineer, it's very helpful po
You're welcome!
6.) THE FUNCTION IS A SOLUTION TO THE DE.
Proving:
Let C1+C3=C4 then,
y=C4e^x + C2e^(2x)
y'=C4e^x + 2C2e^(2x)= y+C2e^(2x)
y''=C4e^x + 4C2e^(2x)= y+3C2e^(2x)
y'''=C4e^x + 8C2e^(2x)= y+7C2e^(2x)
Substituting,
y'''-6y''+11y'-6y=0
[y+7C2e^(2x)]-6[y+3C2e^(2x)]+11[y+C2e^(2x)]-6y=0
y+7C2e^(2x)-6y-18C2e^(2x)+11y+11C2e^(2x)-6y=0
[y-6y+11y-6y]+(7-18+11)[C2e^(2x)]=0
0y+0[C2e^(2x)]=0
0=0
Therefore, the given function is a solution to the differential equation.
Good job!
Oh i see.. Oo nga pala, we can combine the two constants since they both have e^x.❤
Engineer ang answer po sa assignment is it is a solution to the D.E hehehehe
CORRECT!
Number 6 It is a Solution to DE
Hi engr paano po pag may integral sign
2years ago na pero magcocomment ako hahahaha. pinahaba mo lng yung sa assignment sir 🥹
tho nag enjoy ako kasi napapractice utak ko hehehe
This is informative! Hats off to you, Sir! I am a HUMSS grad, currently taking an engineering program kaya medyo nahirapan ako sa Calc. Btw, pwede po malaman kung saan po ang source or book po neto, for review na din po. TIA. I subscribed!
Same
Elementary Differential equations by Rainville
U are the best thank you 💗💗💗💗
Is a solution to De Engr..👌
meron po ba kayo explanation papano nakuha ang assignment engineer? hindi ko po kase nakuha kase naguguluhan ako
Sure. Where shall I send it?
Pa send ng solution sa assignment?
Idol ano po gamit mo na desktop?kase I want to use the same sa inyo while making notes.
Gaming PC itong gamit ko since kapatid ko ang nagbuild 😊
Ahh ok, Yung software po?
@@kimcaesar2659 movavi software po
Pwede po ba sa ex no.2 na I transpose yung negative sa right side para equal din sila sa left? Kahit hindi 0=0 ang answer? Ans: 4c1cos2x+4c2sin2x = 4c1cos2x+4c2sin2x
Yes po. As long as nasatisfy ang equation is okay lang.
ASSIGNMENT: It is a SOLUTION to DE.
Sagot sa assignment i tried it yes got it zero equals zero haha is a solution to a D.E
Not a solution,Tama poba?
Can someone send me the solution for the assignment pls haha
Nakakamatay to pag d mo memorize yung trigonometric functions 😭
Kaya yan!
Hello po sir, paano po kung 2 variables na yung differential equation? For example po y=Ax+Be^x; (x-1)y''-xy'+y=0
Same lang po na 2 constants = 2 times mag dederive.
6. 0=0 it is a solution of DE po
is it not a solution?
4c1e^2x=0 final answer ko eh
y = C1e^x + C2e^2x + C3e^x
y' = C1e^x + 2C2e^2x + C3e^x
y'' = C1e^x + 4C2e^2x + C3e^x
y''' = C1e^x + 8C2e^2x + C3e^x
Substitute:
C1e^x + 8C2e^2x + C3e^x - 6(C1e^x + 4C2e^2x + C3e^x) + 11(C1e^x + 2C2e^2x + C3e^x) - 6(C1e^x + C2e^2x + C3e^x) = 0
C1e^x + 8C2e^2x + C3e^x - 6C1e^x - 24C2e^2x + 6C3e^x + 11C1e^x + 22C2e^2x + 11C3e^x - 6C1e^x - 6C2e^2x - 6C3e^x = 0
add common terms:
11C1^x - 11C1^x + 2C2e^2x - 2C2e^2x + 11C3e^x - 11C3e^x = 0
0 = 0 ✔
@@cepcep5363 same
It's a solution
A solution po yung number 6
Solution :D