3. Linear First-Order Differential Equations A first-order differential equation is said to be linear if it can be expressed in the form : Where and are functions of x.
4. To solve a first-order linear equation, first rewrite it (if necessary) in the standard form above then multiply both sides by the integrating factor
5. The resulting equation, Is then easy to solve, not because it’s exact, but because the left-hand side collapse.
6.
7. Therefore, the general equation becomes Making it susceptible to an integration, which gives the solution : Do not memorize this equation for the solution ; memorize the step needed to get there.