Find the series solution (centered at zero) to the differential equation y'+12xy=0. Find the general term of the series and identify it as the sum, product, quotient, or composition of the library of algebraic and/or transcendental functions.

Question

anonymous · Answer

To get an idea of the solution, notice that your DE is a separable on
$$y'+12xy=0\
\frac {y'}y=-12 x\

$$

anonymous · Answer

$$
\ln(y/c) = -6 x^2\
y= c e^{-6 x^2}
$$

anonymous · Answer

Your series solutions, also will give you that.
Try to do it.

anonymous · Answer

Your series should look like
$$c-6 c x^2+18 c x^4-36 c x^6+54 c
   x^8-\ \frac{324 c
   x^{10}}{5}+O\left(x^{11}\right
   )
$$

anonymous · Answer

Would i start with |dw:1416875292750:dw|