Need help solving simple Differential problem (help)

[Jennifer_88]

Hi,

I am working out a heat transfer problem but i've to solve the Differential equation in order to keep going on but it's been a long time since i did any Differential. your help will be appreciated.

the equation in heat transfer form is T^2+z*k*T=z(C1*x+C2)

or

d^2y/dx+z*k*dy/dx=z(C1*x+C2)

z & k are constants, the equation need to be solved in terms of y(x)

[Delta²]

if you set f=dy/dx then it becomes df/dx+zkf=z(c_1x+c_2). You multiply by the integrating factor e^{zkx} and get
(f(x)e^{zkx})'=ze^{zkx}(c_1x+c_2)

and by integrating both sides and solving for f(x) you ll get

f(x)=\frac{z\int c_1xe^{zkx}dx+ z\int c_2e^{zkx}dx+ c_3}{e^{zkx}}. You just have to compute the integrals which seem easy and get f(x). You then find y(x)=\int f(x)dx

[Jennifer_88]

where did C3 come from ?? thanks for the help

[Delta²]

where did C3 come from ?? thanks for the help
It is the integration constant. You can calculate by the initial condition for f(=dy/dx). You ll have another c4 constant from the integration of f to find y.