## Section 9.3: Separable differential equations Lecture Video

###
1. Find the general solution of the following differential equation.

### (a) \(\displaystyle\frac{dy}{dx}=6x\sqrt{y}\) solution

### (b) \(\displaystyle \frac{dy}{dx}= \frac{1+\sin(x)}{y}\) solution

### (c) \(\displaystyle \frac{dy}{dx}= \frac{x+1}{xy}\)
solution

### (d) \(\displaystyle \frac{d u}{d t}=\frac{2+t^{4}}{u^3 t^{2}+u^{4} t^{2}}\) solution

### 2. Find the solution of the differential equation that
satisfies the given initial condition.

### (a) \(\displaystyle \frac{dy}{dx}=2y, \: \:
y(1)= e\) solution

### (b) \(\displaystyle \frac{dy}{dx}= xe^y, \: \: y(0)= 0\) solution

### (c) \(\displaystyle \frac{dy}{dx}=\frac{3}{1+x^2}, \:\: y(1)=\pi\)
solution

### 3. Find an equation of the curve that passes through the point \((1, 3)\) and whose slope at \((x, y)\) is \(\dfrac{x}{y}\). solution