Solve the following differential equation for the general solution:

{eq}\displaystyle \frac{dy}{dx} = e^{2x} {/eq}

Question:

Solution of the Differential Equation :

We have various methods to find the general solution of differential equations:

(i) By separation of variables

(ii) By homogeneous differential equations

(iii) By exact differential equations

(iv) By linear differential equations

To find the solution of the differential equation we use the method of separation of variables. We can solve this by separating the equation into two parts. We move all of the equation involving the {eq}y{/eq} variable to one side and all of the equation involving the {eq}x{/eq} variable to the other side, then we can integrate both sides as

{eq}\int P(y)\: dy=\int Q(x)\: dx {/eq}

Answer and Explanation: 1