Questions

01

Homogeneous?

Is $x{y}^{\prime }=y+2x{e}^{-y/x}$ a homogeneous differential equation?

02

Transform linear quotient to homogeneous

Transform this equation to a homogeneous equation:

$$\frac{dy}{dx}=\frac{x+y+4}{x-y-6}.$$

03

Integrating factor

Check that $x{y}^2$ is an integrating factor for $(2y-6x)dx+(3x-4x^2{y}^{-1})dy=0$.

04

Reduction of order

Reduce the order of the following two differential equations. (No need to solve them.)

• (a) $x{y}^{\prime \prime }-y^{\prime }=3x^2$
• (b) $y{y}^{\prime \prime }=(y^{\prime }{)}^2$