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 2 years ago
dy/dx+3y=7 y(0)=0
Find a particular solution to the nonhomogeneous differential equation.
 2 years ago
dy/dx+3y=7 y(0)=0 Find a particular solution to the nonhomogeneous differential equation.

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chambek
 2 years ago
Best ResponseYou've already chosen the best response.0Also.....Find the solution to the initial value problem. I'm trying to learn this on my own but really am just not getting it.

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\mathrm dy}{\mathrm dx}+3y=7\] is a linear equation of the from \[\frac{\mathrm dy}{\mathrm dx}+p(x)y=q(x)\] to solve the linear equation we need an integrating factor \[\mu(x)=e^{\int p(x)\text dx}\] then \[\frac{\mathrm d}{\mathrm dx}\big(\mu(x)y\big)=\mu(x) q(x)\]\[\mu(x)y=\int{\mu(x) q(x)\text dx} \] \[y=\quad\dots\]

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1after integration you will have a constant of integration, substituting the initial value will allow you to find it

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0I got the first part! Thanks, I'm trying to get the part with the initial value now....where do i substitute that in?

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1y = y(x) the condition is y(0) = 0 which means (x,y) = (0,0) is a solution

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0ok....doing that I got 0....and that was wrong, it is asking for a y=..... I'm sorry i dont understand my professor at all so i essentially now nothing about diffe q's

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0or grammar apparently....

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1can you show some working

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0sure, so i got (7/3) as the particular solution to the nonhomogeneous equation. then going from there, I included a C in my integral so I could plug in 0 for y and solce for c, then get an equation for y=.... \[3y=7+C\] I found C to be 7 at y(0)=0 giving me \[3y=77\] which just doesnt really make too much sense, but I tried 0 regardless and realized I have no clue what I'm doing haha

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0oh no wait a second....hold on

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0grrr nevermind, that still got me 0, I had made a mistake in my algebra......

UnkleRhaukus
 2 years ago
Best ResponseYou've already chosen the best response.1\[\frac{\mathrm dy}{\mathrm dx}+3y=7\]\[\mu(x)=e^{\int 3\text dx}=e^{3\int \text dx}=e^{3x}\]\[\frac{\mathrm d}{\mathrm dx}\big(e^{3x}y\big)=7e^{3x}\] \[e^{3x}y=\int{7 e^{3x}\text dx}=7\int e^{3x}\text dx=7\frac{e^{3x}}3+c\] \[y=\frac73+ce^{3x}\] \[y(0)=0\] \[0=\frac73+c\]\[c=\frac73\] \[y=\frac73\frac73e^{3x}\]

chambek
 2 years ago
Best ResponseYou've already chosen the best response.0..............so, i got that awhile ago, and I kept putting the answer in as you have it, but, the equation is in terms of t.......*facepalm* thanks for the help!
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