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June 3rd, 2012, 01:52 AM  #1 
Member Joined: Apr 2012 Posts: 47 Thanks: 0  differential equation use substitution methode
for this equation i use substitution methode. but my answer is not right. dont know where i make a mistake, please someone can help me to check. thanks! right answer is y=4x ln(cx) 
June 3rd, 2012, 02:43 AM  #2 
Member Joined: Apr 2012 Posts: 47 Thanks: 0  Re: differential equation use substitution methode
i have an other question last step i dont get it, where is u' and +u get from? what is the u'? 
June 3rd, 2012, 02:50 AM  #3 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differential equation use substitution methode
U=Y*1/x+4 x*U4=Y Its the mistake in your previous question 
June 3rd, 2012, 03:05 AM  #4 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differential equation use substitution methode
x*y'=y+4*x x*dy=y*dx+4x*dx x*dyy*dx=4x*dx (x*dyy*dx)/(x^2) = (4/x)*dx d(y/x) = (4/x)*dx, integrating both sides, y/x+c1 = 4ln(x)+c2 y=4xln(x)+Cx where C=c1c2 My C = your 4ln(c) 
June 3rd, 2012, 03:49 AM  #5  
Member Joined: Apr 2012 Posts: 47 Thanks: 0  Re: differential equation use substitution methode Quote:
Quote:
 
June 3rd, 2012, 04:03 AM  #6 
Math Team Joined: Nov 2010 From: Greece, Thessaloniki Posts: 1,990 Thanks: 133 Math Focus: pre pre pre pre pre pre pre pre pre pre pre pre calculus  Re: differential equation use substitution methode [color=#000000]What mathbalarka has done..... remember that , now for .[/color] 
June 3rd, 2012, 04:16 AM  #7 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differential equation use substitution methode
y'=1y/x x*y'=xy x*y'+y=x x*y'+x'*y=x (xy)'=x d(xy)=x*dx integrating, xy+c1=x^2/2+c2 xy=x^2/2+C y=x/2+C/x 
June 3rd, 2012, 04:21 AM  #8 
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differential equation use substitution methode
If you want, I can tell you the solution of a,b are constants Note: sorry for writing answers of previous questions without using 
June 3rd, 2012, 08:42 AM  #9 
Member Joined: Apr 2012 Posts: 47 Thanks: 0  Re: differential equation use substitution methode thx problems solved. now got an other one problem. how do i found out C is just C not lnC? how can i recognize it after intergration? example: other one confused 
June 3rd, 2012, 10:02 AM  #10  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: differential equation use substitution methode Quote:
According to my calculations, The genarel solution of is:  

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