Answer:
Step-by-step explanation:
Enter numbers or scientific notation.
For scientific notation, use a carat ^ for the powers of 10 or use e notation.
Scientific Notation: 3.45 x 10^5
E Notation: 3.45e5
Answer:
2x+9=-17
Step-by-step explanation:
hopefully this helps :)
Answer:
Linear and non-homogeneous.
Step-by-step explanation:
We are given that
![\frac{xy'}{(x^2+7)y}=cosx+\frac{e^{3x}}{y}](https://tex.z-dn.net/?f=%5Cfrac%7Bxy%27%7D%7B%28x%5E2%2B7%29y%7D%3Dcosx%2B%5Cfrac%7Be%5E%7B3x%7D%7D%7By%7D)
We have to convert into y'+P(x)y=g(x) and determine P(x) and g(x).
We have also find type of differential equation.
![y'=\frac{(x^2+7)y}{x}(cosx+\frac{e^{3x}}{y}}](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7B%28x%5E2%2B7%29y%7D%7Bx%7D%28cosx%2B%5Cfrac%7Be%5E%7B3x%7D%7D%7By%7D%7D)
![y'=\frac{(x^2+7)cosx}{x}y+\frac{(x^2+7)e^{3x}}{x}](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7B%28x%5E2%2B7%29cosx%7D%7Bx%7Dy%2B%5Cfrac%7B%28x%5E2%2B7%29e%5E%7B3x%7D%7D%7Bx%7D)
![y'-\frac{cosx(x^2+7)}{x}y=\frac{e^{3x}(x^2+7)}{x}](https://tex.z-dn.net/?f=y%27-%5Cfrac%7Bcosx%28x%5E2%2B7%29%7D%7Bx%7Dy%3D%5Cfrac%7Be%5E%7B3x%7D%28x%5E2%2B7%29%7D%7Bx%7D)
It is linear differential equation because this equation is of the form
y'+P(x)y=g(x)
Compare it with first order first degree linear differential equation
![y'+P(x)y=g(x)](https://tex.z-dn.net/?f=y%27%2BP%28x%29y%3Dg%28x%29)
![P(x)=-\frac{cosx (x^2+7)}{x},g(x)=\frac{e^{3x}(x^2+7)}{x}](https://tex.z-dn.net/?f=P%28x%29%3D-%5Cfrac%7Bcosx%20%28x%5E2%2B7%29%7D%7Bx%7D%2Cg%28x%29%3D%5Cfrac%7Be%5E%7B3x%7D%28x%5E2%2B7%29%7D%7Bx%7D)
![\frac{dy}{dx}=\frac{(x^2+7)(ycosx+e^{3x})}{x}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7B%28x%5E2%2B7%29%28ycosx%2Be%5E%7B3x%7D%29%7D%7Bx%7D)
Homogeneous equation
![\frac{dy}{dx}=\frac{f(x,y)}{g(x,y)}](https://tex.z-dn.net/?f=%5Cfrac%7Bdy%7D%7Bdx%7D%3D%5Cfrac%7Bf%28x%2Cy%29%7D%7Bg%28x%2Cy%29%7D)
Degree of f and g are same.
![f(x,y)=(x^2+7)(ycosx+e^{3x}),g(x,y)=x](https://tex.z-dn.net/?f=f%28x%2Cy%29%3D%28x%5E2%2B7%29%28ycosx%2Be%5E%7B3x%7D%29%2Cg%28x%2Cy%29%3Dx)
Degree of f and g are not same .
Therefore, it is non- homogeneous .
Linear and non-homogeneous.
2y-4=3y-5
-4=y-5
1=y
Answer: y=1
1/1.5 * 10^-6 = 2500/x
x = 1.5 * 10^-6 * 2500
x = 0.00375 or 3.75 * 10^-3 second.