13. Intro to Differential Equations

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.

Which of the following is the solution to the differential equation $\frac{dy}{dx}=4xy$, where $y\left(2\right)=-2$?

Solve the following system of differential equations by systematic elimination:

$$\frac{\partial x}{\partial t}=2x-y$$$$\frac{\partial y}{\partial t}=x$$
Which of the following gives the general solution for $x\left(t\right)$?

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

33–42. Solving initial value problems Solve the following initial value problems.

p'(x) = 2/(x² + x), p(1) = 0

Consider the following differential equation: $x\frac{dy}{dx}-y=x^2\sin \left(x\right)$. Which of the following is the correct integrating factor to solve this equation?

Find the general solution of the differential equation: $y^{\left(4\right)}-2y^{\left(2\right)}+y=0$.