HL1 CFU 8.3

If you are solving differential equations and have just isolated the variables, dy and dx to their respective sides, what do you do next?

• Integrate both sides and then include +c to both sides.

• Integrate both sides and then include +c to the x side.

• Integrate both sides and then include +c to the y side.

Determine the value of "c" that satisfies the differential equation  $\frac{dy}{dx}=\frac{x+1}{y+2}$  if the curve goes through the point (0, -1).

• 5/2

• -3/2

• -1/2

• 1

Solve the differential equation for y given the initial value. 
 $\frac{dy}{dx}=\frac{4x}{y},\ y\left(0\right)=1$ 

•  $y=\sqrt{4x^2-4}$  

•  $y=2x^2+1$  

•  $y=e^{2x^2}$  

•  $y=\sqrt{4x^2+1}$  

Find the particular solution for 
 $\frac{dy}{dx}=2x\sqrt{y}$  given the point  $\left(3,4\right)$ .

•  $2\sqrt{y}=x^2+c$  

•  $y=\frac{\left(x^2+25\right)^2}{4}$  

•  $y=\left(\frac{x^2-5}{2}\right)^2$  

•  $y=\frac{x^2+5}{2}$ 

 Find the general solution for
 $\frac{dy}{dx}=\frac{2x}{e^{2y}}$  

•  $y=\frac{\ln\left(x^2+c\right)}{2}$  

•  $y=\ln\left(2x^2+c\right)$  

•  $y=e^{2x}+c$  

•  $y=\frac{\ln\left(2x^2+c\right)}{2}$