Separable first order differential equations Quiz

1. Find the general solution of $\frac{dy}{dx}=3y$.

• A. $y=3Ax$
• B. $y=Ae^{3x}$
• C. $y=e^{3x}+A$
• D. $y=3\ln x+A$

2. Which is the correct integrated form of $\frac{dy}{dx}=\frac{x^2}{y^3}$?

• A. $\frac{y^2}{2}=\frac{x^3}{3}+c$
• B. $y^4=x^3+c$
• C. $\frac{y^4}{4}=\frac{x^3}{3}+c$
• D. $\ln y^3=\ln x^2+c$

3. $\frac{dy}{dx}=\frac yx$ for $x,y>0$, with $y=6$ when $x=2$. Find $y$.

• A. $y=3x$
• B. $y=x+4$
• C. $y=x^2+2$
• D. $y=\frac{12}{x}$

4. Find the general solution of $\frac{dy}{dx}=e^{x-y}$.

• A. $y=x+c$
• B. $e^{y}=xe^{x}+c$
• C. $y=e^{x}+c$
• D. $e^{y}=e^{x}+c$

5. $\frac{dy}{dx}=6x\sqrt y$ and $y=4$ when $x=0$. Find $y$ when $x=1$.

• A. $49$
• B. $12.25$
• C. $7$
• D. $3.5$