# Ln Equations Formation

• Oct 7th 2007, 02:33 AM
Simplicity
Ln Equations Formation
I need help with these four questions (If possible, can it be explained in steps):

1.
$\displaystyle \sin x \frac{\mathrm{d}y}{\mathrm{d}x} = e^y,$ $\displaystyle 0<x<\pi,$ $\displaystyle y=0 at x=\frac{\pi}{2}$

2.
$\displaystyle \sin x \frac{\mathrm{d}y}{\mathrm{d}x} = \tan y (3\cos x + \sin x),$ $\displaystyle y=\frac{\pi}{6} at x=\frac{\pi}{2}$

3.
$\displaystyle (5-3\sin x) \frac{\mathrm{d}y}{\mathrm{d}x} = 40\cos x,$ $\displaystyle y=0 at x=\frac{3\pi}{2}$

4.
$\displaystyle \frac{1}{y} \frac{\mathrm{d}y}{\mathrm{d}x} = x + xy,$ $\displaystyle y=1 at x=0$
• Oct 7th 2007, 05:13 AM
red_dog
1) $\displaystyle \displaystyle\frac{dy}{e^y}=\frac{dx}{\sin x}$
$\displaystyle \displaystyle\int\frac{dy}{e^y}=\int\frac{dx}{\sin x}$

2) $\displaystyle \displaystyle\frac{dy}{\tan y}=\frac{3\cos x+\sin x}{\sin x}dx$
$\displaystyle \displaystyle\int\cot ydy=\int(1+3\cot x)dx$

3) $\displaystyle \displaystyle\frac{dy}{y(y+1)}=xdx$
$\displaystyle \displaystyle\int\frac{dy}{y(y+1)}=\int xdx$

Now, integrate.