Exercises for Question Type 2: Solving separable differential equations - IB | RevisionDojo

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Question Type 2: Solving separable differential equations

Question Type 2: Solving separable differential equations Exercises

Question 1

Solve the differential equation $\frac{dy}{dx}=y^2\sin x$ , given $y\bigl(\tfrac{\pi}{2}\bigr)=1$ .

[6]

Question 2

Solve the differential equation $\frac{dy}{dx}=\frac{x e^{-x}}{y}$ , given $y(0)=2$ .

[6]

Question 3

Solve the differential equation $\frac{dy}{dx}=(4x+1)y^2$ (general solution).

[5]

Question 4

Solve the differential equation $\frac{dy}{dx}=\frac{y+1}{x}$ , given $y(1)=0$ .

[4]

Question 5

Solve the differential equation $\frac{dy}{dx}=2x\,y$ , given $y(1)=2$ .

[5]

Question 6

Solve the differential equation $\frac{dy}{dx}=\frac{x}{y}$ .

[4]

Question 7

Solve the differential equation $\frac{dy}{dx}=(4x+1)y^2$ , given $y(0)=1$ .

[5]

Question 8

Solve the differential equation $\frac{dy}{dx}=\frac{y}{1+x^2}$ , given $y(0)=3$ . [5 marks]

[5]

Question 9

Solve the differential equation $\frac{dy}{dx}=\frac{2x+3}{3y^2-1}$ , given $y(0)=0$ .

[6]

Question 10

Solve the differential equation $\frac{dy}{dx}=\frac{3x^2+2}{y^3}$ .

[5]

Question 11

Solve the differential equation $\frac{dy}{dx}=x^2e^x\,y$ , given $y(0)=1$ .

[6]

Question 12

Solve the differential equation $\frac{dy}{dx}=\frac{5x^4-2x}{y^3}$ .

[5]