13. Intro to Differential Equations

Solve the differential equation by separation of variables: $\frac{dy}{dx}=x(1-y^2)$. Which of the following is the general solution?

What is the general solution to the differential equation $\frac{dy}{dx}=8e^{4x^2}cos\left(2y\right)$?

Solve the differential equation $\frac{ds}{dr}=ks$ by separation of variables. Which of the following is the general solution?

Solve the initial-value problem for the homogeneous differential equation: $x y^2 \frac{dy}{dx}=y^3-x^3$, with $y\left(1\right)=3$. What is the explicit solution?

Solve the differential equation by variation of parameters: $y^{″}+y=\sec \left(x\right)\tan \left(x\right)$. Which of the following is the general solution?

Consider the differential equation $\frac{dy}{dx}=xy+x$. Which of the following best describes this equation?

What is the general solution to the differential equation $\frac{dy}{dx}=x-13y^2$ for $y>0$?

Solve the differential equation $y^{\text{'}\text{'}}+y=\sin \left(x\right)$ using the method of variation of parameters. Which of the following is the general solution?

Find the general solution of the second-order differential equation $3y^{″}+2y^{\prime }+y=0$.

Solve the initial-value problem for the homogeneous differential equation: $(x^2+2y^2)\frac{dx}{dy}=xy$, with $y(-1)=3$. What is the explicit solution for $x$ in terms of $y$?

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

Solve the differential equation $y^{\text{'}\text{'}}+2y^{\text{'}}=2x+7-e^{-2x}$ using the method of undetermined coefficients. 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.

Solve the differential equation $x\frac{dy}{dx}=6y$ by separation of variables.