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- #1

So if you are given a single order differential equation, and asked to find the general solution, what do you do differently?

eg: $$ \frac {dy}{dx} - y = e^{3x} $$

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- Thread starter
- #1

So if you are given a single order differential equation, and asked to find the general solution, what do you do differently?

eg: $$ \frac {dy}{dx} - y = e^{3x} $$

- Jan 26, 2012

- 890

Nothing.

So if you are given a single order differential equation, and asked to find the general solution, what do you do differently?

eg: $$ \frac {dy}{dx} - y = e^{3x} $$

CB

- Jan 26, 2012

- 39

$\frac {dy}{dx} - y = e^{3x}$

In this case you have a linear differential equation.

If you wanted the general solution for a linear differential equation then you need to recognize the general form $\frac {dy}{dx} + P(x)y=Q(x)$ , and work with that.

If you are asking about a particular diff. eq then the general solution is nothing more than what you have described.

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$\frac {dy}{dx} - y = e^{3x}$

In this case you have a linear differential equation.

If you wanted the general solution for a linear differential equation then you need to recognize the general form $\frac {dy}{dx} + P(x)y=Q(x)$ , and work with that.

If you are asking about a particular diff. eq then the general solution is nothing more than what you have described.

The particular solution is the single solution of the Differential Equation that satisfies BOTH the DE AND the initial/boundary conditions.

So if you are given a single order differential equation, and asked to find the general solution, what do you do differently?

eg: $$ \frac {dy}{dx} - y = e^{3x} $$

Hi! When you are given conditions in the problem, for example y(0)=1 and y'(0)=0, you substitute this to the general solution which refers to the solution you have obtained from seperating and differentiating and you will obtain your partial solution