# Need help solving simple Differential problem (help)

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
Homework Helper
Gold Member
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 $$y(x)=\int f(x)dx$$

where did C3 come from ?? thanks for the help

Delta2
Homework Helper
Gold Member
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.