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Differential Equation isolation

  • Thread starter Lanza52
  • Start date
  • #1
63
0
Solve the differential equation:

[tex]\frac{dy}{dx}-\frac{y}{x}=3x^{2}[/tex]

Where y(1)=3

Can't figure out how to isolate each side. Played with it forever to no success. Any tips?
 

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
...whenever you have a function of the form:

[tex]\frac{dy}{dx}+Py=Q[/tex] where both P and Q are functions of x..
you multiply throughout by [itex]e^{\int P dx}[/itex] and then integrate both sides with respect to x...

HINT: When you multiply throughout by [itex]e^{\int P dx}[/itex] and then integrate both sides with respect to x

The left hand side becomes [itex]ye^{\int P dx}[/tex]
 
  • #3
90
0
If you wanna use separation of variables you can solve the complimentary equation and use variation of parameters.
 

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