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Physical Applications

الكلية كلية العلوم     القسم قسم الفيزياء     المرحلة 2
أستاذ المادة محسن كاظم مطلب الجنابي       6/8/2011 6:39:01 AM

Physical Applications

 

Ex.8 : Find the differential equation for a body which falls freely ?

 

Ex.9 : A radiant Source has a decreasing time average for degenerated nuclei with respect for initial number of nuclei . Find the equation of  degeneration ?

 

Ex.10: A capacitor charges with a charge (q) which its value is ( C) and discharges from its charge into a resistance (R ) .Find the equation of the circle  and solve it ?

 

 

 

 

Non Homogenous First Order Differential Equations:

 

1-Integrating Factor Method .

 

Ex 1: Solve the  differential equation  1¤x . dy ¤ dx + 2y / 1+x² =3 by integrating factor method ?

 

Ex2 :  Solve the  differential equation   dy/dx-e^-x2 = -2yx    by integrating factor method ?

 

Ex3:  Solve the  differential equation  x². dy/dx –cosx = -2yx   by integrating factor method ?

 

Ex4:  Solve the  differential equation  dy/dx - ytanx =  e^sinx   by integrating factor method ?

 

Ex5:  Solve the  differential equation  dy/dx +2yt-e^-t2 = 0  by integrating factor method ?

 

Ex6:  Solve the  differential equation  dy/dx – t = 2ty  by integrating factor method ?

 

 

     Ex7:  Solve the  differential equation  t².dy/dt – cost = -2ty  by integrating    factor method ?

 

 

Physical Applications

 

Ex.8 : A resistance which its value is ( R ) and connects successively to a capacitor which its capacity is ( C) and they are joined up to a battery has a constant voltage which its value is ( E ) . Find the differential equation which ascribes the electrical circle and solve it ?  

 

 

 

Ex.9 : An electrical circle consists of a coil which its inductive  coefficient is ( L ) and a resistance which its value is ( R ) , they connect successively and join the battery that its voltage is ( E ) . Find the differential equation which ascribes the case and solve it ?