Is there an effective method of checking a solution to a differential equation once you have solved it (or thought you have)? Using a calculator or even MathCAD.
Both implicitly and explicitly and with the use of an arbitrary constant?
Is there an effective method of checking a solution to a differential equation once you have solved it (or thought you have)? Using a calculator or even MathCAD.
Both implicitly and explicitly and with the use of an arbitrary constant?
If you solve this equation for example you get $\displaystyle y=\frac{c}{sinx}+7$ where c i s a constant.
Now find that $\displaystyle y'=-c\frac{cosx}{(sinx)^2}$.
Your differential equation is $\displaystyle (tanx)y'+y=7$ and you know both y and y', apply them and you will see that it is true
That's a strange question. The answer- by doing exactly what it says! Differentiate whatever y you have (using implicit differentiation if necessary) and put y and its derivative into that equation. If the problem is that you cannot differentiate your y, what is your y?
I'm sorry for giving up. I'm getting really stressed out with the maths I'm trying to learn and and some aspects of this forum, but more on topic: I used the equation above as an example - the thing I wanted to check is this:
$\displaystyle \sqrt{t^2+9}\frac{dy}{dt}=y^2$
I thought i'd solved it with:
$\displaystyle y=\frac{1}{ln(t+\sqrt{t^2+9})+C}$
It's probably wrong - but I wondered whether there was an easy way of checking whether or not it was correct before trying to solve for C to find the value of the arbitrray constant for when y(0)=1
Hmmmm...
My course has given me a book of all the things I need to know when it comes to exam - it's like the bible - lol.
I have not came across sinh.
In the section showing the standard integrals, it gives me:
$\displaystyle \int\frac{1}{\sqrt{t^2+a^2}}dt=ln(x+\sqrt{x^2+a^2} )$
Could this be the same thing in a different format?
If only you had posted the real question (quoted above) in the first place, a lot of time (and frustration on your part) might have been avoided.
As you have discovered the hard way, both answers are correct. It is not uncommon for somethng like this to happen. You should research hyperbolic functions and inverse hyperbolic functions, just to fill out some useful mathematical background you haven't been formally taught.