Browse Questions

Find the differential equation of family of straight lines $y=mx+\large\frac{a}{m}$ When $a$ is the parameter.

Toolbox:
• If we have an equation $f(x,y,c_1,c_2,....c_n)=u$ Containing n arbitrary constant $c_1,c_2...c_n$, then by differentiating n times, we get $(n+1)$ equations in total. If we eliminate the arbitrary constants $c_1,c_2....c_n,$ we get a D.E of order n
Step 1:
$y=mx+\large\frac{a}{m}$ where a is the parameter
Step 2:
$\large\frac{dy}{dx}$$=m$
It is the required D.E