Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
qila
Group Title
verify that y=(4e^3x) 2 is an explicit solution of differential equation y'3y=6
 2 months ago
 2 months ago
qila Group Title
verify that y=(4e^3x) 2 is an explicit solution of differential equation y'3y=6
 2 months ago
 2 months ago

This Question is Open

esamalaa Group TitleBest ResponseYou've already chosen the best response.0
use the variable separation to solve this D E
 2 months ago

qila Group TitleBest ResponseYou've already chosen the best response.0
can you try to solve it and explain more about it?
 2 months ago

esamalaa Group TitleBest ResponseYou've already chosen the best response.0
i think that's the right solution
 2 months ago

VeritasVosLiberabit Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{ dy }{ dx }=6+3y\] \[\frac{ dy }{ 6+3y }=dx\] \[\int\limits_{}^{}\frac{ dy }{ 6+3y }=\int\limits_{}^{}dx\] \[\frac{ 1 }{ 3 }\ln(6+3y)+C _{1}=x+C _{2}\]
 2 months ago

VeritasVosLiberabit Group TitleBest ResponseYou've already chosen the best response.0
\[\ln(6+3y)=3x+C\] \[e ^{\ln(6+3y)}=e ^{3x+C}\] \[6+3y=e ^{3x}e ^{C}\] \[3y=Ce ^{3x}6\] \[y=Ce ^{3x}2\]
 2 months ago

VeritasVosLiberabit Group TitleBest ResponseYou've already chosen the best response.0
I think you need to know an intial value y_0 to find C = 4.
 2 months ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
This question does not ask you to solve the DE, it asks to verify that a given solution solves the DE.
 2 months ago

UnkleRhaukus Group TitleBest ResponseYou've already chosen the best response.1
The function \[y(x)=4e^{3x} 2\] its derivative\[y'(x) = 12e^{3x}\] The differential equation \[\qquad y'3y\qquad \quad =6\] Plugging the function and its derivative into the DE\[\begin{align} [12e^{3x}]3[4e^{3x} 2]&=6\\ 12e^{3x}12e^{3x} +6&=6\\ 6&=6\\ 0&=0 \end{align}\](a true statement) Hence \(y=4e^{3x} 2\) is an explicit solution to the differential equation.
 2 months ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.