13. Intro to Differential Equations

Find the general solution of the differential equation: $x^2{y}^{\prime }+x(x+2)y=e^x$.

Find the general solution of the differential equation $y^4+y^3+y^2=0$.

Solve the differential equation by variation of parameters: $y^{″}+y=\sin ⁠2x$. What is the general solution $y\left(x\right)$?

Find the general solution of the differential equation: ${\cos }^2\left(x\right)\sin \left(x\right)\frac{dy}{dx}+({\cos }^3(x\left)\right)y=1$.

Solve the differential equation using variation of parameters: $y^{″}-16y=16x{e}^{4x}$. Which of the following is the general solution?

Solve the differential equation $4y^{″}+y^{\prime }+y=x^2-5x$ using the method of undetermined coefficients. What is the general solution?

Find the general solution of the differential equation $(1+x)\frac{dy}{dx}-xy=x+x^2$.

Of the following, which is not a solution to the differential equation $y^{″}+9y=0$?

Suppose that $y\left(x\right)$ solves the ordinary differential equation $\frac{dy}{dx}=3y$ with the initial condition $y\left(0\right)=2$. What is $y\left(x\right)$?

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

Solve the differential equation by separation of variables: $\frac{dy}{dx}=\frac{2y+7}{8x+9}$. Which of the following is the general solution?

Solve the differential equation using variation of parameters: $y^{\text{'}\text{'}}-2y^{\text{'}}+y=e^t\arctan \left(t\right)$. Which of the following is the general solution?

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

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?

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