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myininaya
 one year ago
Best ResponseYou've already chosen the best response.0Do you mean solve the IVP?

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0The way I approach such a problem: Solve the homogenous part of the differential equation first: \[\Large y''(x)=0 \] So the solution to this, almost trivial DE is: \[\Large y_g(x)=Cx+K \] Where C and K are constants of integration. Now you need to find the particular solution to the homogenous differential equation. This is usually done by guessing. Since: \[\Large y''(x)=1e^{2x} \] A 'okay' guess could be: \[\Large y_p(x)=A+Be^{2x} \] Notice here that this is not yet good enough, see the solution already obtained above. We have Cx + K. So, in order to not overlap any solutions, we want to increase the linear exponent again: \[\Large y_p(x)=Ax^2+Be^{2x} \] Now this is a good guess. Substituting back will give you: \[\Large 2A+4Be^{2x}=1e^{2x} \] From which you can obtain that: \[ \Large A= \frac{1}{2}, \ B= \frac{1}{4}\] So given by the principle of superposition you have: \[\Large y(x)=y_p(x)+y_g(x)=Cx+K+\frac{1}{2}x^2\frac{1}{4}e^{2x} \]

Craig4242
 one year ago
Best ResponseYou've already chosen the best response.0I am not yet familiar with the methods you demonstrated above. Here is the answer I get: \[^{x^2/2}^{e^2x/4}+^{e^2/4}x(1/2)\]

Craig4242
 one year ago
Best ResponseYou've already chosen the best response.0As I am new to typing equations, I wonder how you made your's look so neat?

Spacelimbus
 one year ago
Best ResponseYou've already chosen the best response.0I recommend you to check out Paul's website then, he has an amazing introduction to the method I suggested above, clearly, it's not the only one to solve this problem. But it makes inhomogeneous differential equations quite straight forward to solve. Here is the link: http://tutorial.math.lamar.edu/Classes/DE/UndeterminedCoefficients.aspx As to \(\LaTeX\). First I use the perimeter \Large to make my equations look bigger, or in the case of this website  just more readable. You can write fraction by typing \frac{nominator}{denominator}

Craig4242
 one year ago
Best ResponseYou've already chosen the best response.0Thanks for the help:)
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