Find the specific solution of the differential equation

Question

Find the specific solution of the differential equation dy/dx=3y/x² with condition y(-3) = e.

• y=e^-3/x
• y=-1-3/x
• y=-e^1/2
• None of these

Answer 1

This DE is separable. If you divide both sides by y ans multiply both sides by dx, you get

 

dy/y = 3/x² dx.

 

Integrate both sides:

 

∫ dy/y = ∫ 3/x² dx

 

ln |y| = -3/x + C.

 

You can then solve for y using algebra. The final answer is y = Ke^-3/x . The details are left you.