Solve the differential equation using variation of parameters: $y^{″}+3y^{\prime }+2y=15+e^x$. Which of the following is the general solution?

Find the general solution of the system of differential equations:

$$\frac{\partial x}{\partial t}=-5x+4y$$$$\frac{\partial y}{\partial t}=3x-3y$$

Solve the differential equation $4x^2{y}^{\text{'}\text{'}}+9x{y}^{\text{'}}+y=x^2-x$ using the method of variation of parameters. Which of the following is the general solution?

Solve the differential equation using variation of parameters: $y^{\mathrm{\text{'}\text{'}}}+3y^{\mathrm{\text{'}}}+2y=\frac{1}{3}+e^x$. Which of the following is the general solution?

Solve the differential equation using variation of parameters: $y^{\mathrm{\text{'}\text{'}}}+3y^{\mathrm{\text{'}}}+2y=17+e^x$. Which of the following is the general solution?

Solve the differential equation $y^{\mathrm{\text{'}\text{'}}}+2y=-18x^2{e}^{2x}$ using the method of undetermined coefficients. Which of the following is a particular solution?

Solve the differential equation: $\frac{dy}{dx}=3x^2{y}^2$. Which of the following is the general solution?

Which of the following is the general solution to the differential equation $3x^2{y}^{\text{'}\text{'}}+6x{y}^{\text{'}}+y=0$ for $x>0$?

Find the general solution of the differential equation: $\frac{dr}{d\theta }+r\sec \left(\theta \right)=\cos \left(\theta \right)$.