Hi
The first question ordinary differential equation whats putting me off, is moving the x's and y's to one side and the cos(x) doesnt help or isnt this needed to intergrate?
The second question not sure how to solve the quadratic equation r^2-r-12
The last question =3e^5t?

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Originally Posted by jjssj
The first question ordinary differential equation whats putting me off, is moving the x's and y's to one side and the cos(x) doesnt help or isnt this needed to intergrate?
First thing to do is divide both sides by $\cos x$

Originally Posted by jjssj

The second question not sure how to solve the quadratic equation r^2-r-12
Find factors of -12 to sum to -1.

is this right for the first question
dy+y=(cos^3xsinx)dx/sinx can intergrate this now?

\displaystyle \begin{align*} \cos{(x)}\,\frac{dy}{dx} + \sin{(x)}\,y &= 2\cos^3{(x)}\sin{(x)} - 1 \\ \frac{dy}{dx} + \frac{\sin{(x)}}{\cos{(x)}}\,y &= \frac{2\cos^3{(x)}\sin{(x)} - 1}{\sin{(x)}} \end{align*}
And this can be solved by multiplying both sides by the integrating factor \displaystyle \begin{align*} e^{\int{\frac{\sin{(x)}}{\cos{(x)}}}\,dx} = e^{-\ln{\left[\cos{(x)}\right]}} = e^{\ln{\left\{\left[\cos{(x)}\right]^{-1}\right\}}} = \frac{1}{\cos{(x)}} \end{align*}