IB Mathematics Analysis and Approaches Question Type 3: Homogeneous Differential Equations Exercises

By substituting $y=vx$, solve the differential equation

$$\frac{dy}{dx}=\frac{5x-2y}{2x+5y}.$$

Solve the differential equation

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

By using the substitution $y=vx$, solve the differential equation

$$\frac{dy}{dx}=(\frac{y}{x}{)}^{1/2}.$$

Solve the differential equation

$$\frac{dy}{dx}=\frac{3y-x}{y+x}$$

Solve the differential equation

$$\frac{dy}{dx}=\frac{2x-y}{x+2y}$$

Solve the differential equation

$$\frac{dy}{dx}=\frac{y}{x}+1.$$

Solve the initial-value problem: $$\frac{dy}{dx}=\frac{y}{x}+2,y(1)=3$$

Find the general solution of the differential equation

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

[6 marks]

Solve the differential equation

$$\frac{dy}{dx}=\frac{2x^2+3xy+y^2}{x^2+xy}$$

Solve the differential equation

$$\frac{dy}{dx}=\frac{y-2x}{y+2x}.$$

Solve the differential equation

$$\frac{dy}{dx}=\frac{y^2+x^2}{xy}.$$

Solve the initial-value problem

$$\frac{dy}{dx}=\frac{2y-x}{y-2x},y(1)=1$$