Find the general solution of the differential equation.

{eq}y'=e^{6x}-8x {/eq}

Question:

Find the general solution of the differential equation.

{eq}y'=e^{6x}-8x {/eq}

Indefinite Integral:

If {eq}y' {/eq} denotes the derivative of the function {eq}y = f(x) {/eq}, then we determine {eq}y {/eq} by obtaining the indefinite integral of {eq}y' {/eq}.

So the solution of the differential equation of the form {eq}y' = f'(x) {/eq} is found by integrating {eq}f'(x) {/eq}:

{eq}y = \displaystyle \int f'(x) \ \mathrm{d}x {/eq}

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

{eq}y' = e^{6x}-8x {/eq} gives us the differential of the function {eq}y {/eq} so we integrate {eq}e^{6x}-8x {/eq} to find the solution of the...

See full answer below.


Learn more about this topic:

Loading...
Indefinite Integrals as Anti Derivatives

from

Chapter 12 / Lesson 11
6.1K

Indefinite integrals, an integral of the integrand which does not have upper or lower limits, can be used to identify individual points at specific times. Learn more about the fundamental theorem, use of antiderivatives, and indefinite integrals through examples in this lesson.


Related to this Question

Explore our homework questions and answers library