Solve the differential equation $\frac{dy}{dx}=2y$ by separation of variables. Which of the following is the general solution?

Find the solution to the differential equation $\frac{dy}{dx}=3y$ with the initial condition $y\left(0\right)=2$.

Which of the following is the general solution to the differential equation $\frac{dy}{dx}=9x^2{y}^2$?

Solve the differential equation by separation of variables: $\frac{dy}{dx}=\frac{2y+5}{{8x+9}^2}$. Which of the following is the general solution?

Solve the differential equation $y^{\mathrm{\text{'}\text{'}}}+2y^{\mathrm{\text{'}}}=2x+9-e^{-2x}$ using the method of undetermined coefficients. Which of the following is a particular solution?

Which of the following is the general solution to the differential equation $y^{\mathrm{\text{'}\text{'}}}+y=5x\sin \left(x\right)$ using the method of undetermined coefficients?

Solve the differential equation $5y″-10y\prime +10y=e^{x}secx$ using the method of variation of parameters. Which of the following is the general solution?

Solve the differential equation $y^{\mathrm{\text{'}\text{'}}}+2y^{\mathrm{\text{'}}}=2x+3-e^{-2x}$ using the method of undetermined coefficients. Which of the following is a particular solution?

Solve the differential equation $e^{x}y\frac{dy}{dx}=e^{-y}+e^{-3x}-y$ by separation of variables.