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Exercises for Question Type 2: Separating a differential equation into two variables - IB | RevisionDojo

Question 1

Find the particular solution of $\frac{\text{d}y}{\text{d}x} = \frac{3x^{2}}{y+1}$ satisfying the initial condition $y(0)=0$ .

[6]

Question 2

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

[5]

Question 3

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

[4]

Question 4

Solve the differential equation $\frac{\text{d}y}{\text{d}x} = y^{2} \sin x$ .

[5]

Question 5

Find the particular solution of $\frac{dy}{dx} = y^{2} \sin x$ satisfying $y(0) = 3$ .

[5]

Question 6

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

[5]

Question 7

Find the particular solution of the differential equation $\frac{dy}{dx} = y e^{x}$ satisfying the initial condition $y(0)=3$ .

[5]

Question 8

The following question is about solving a first-order differential equation using the method of separation of variables.

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

[4]

Question 9

Solve the differential equation $\frac{dy}{dx} = \frac{3x^{2}}{y+1}$ .

[4]

Question 10

This question assesses the student's ability to solve a first-order separable differential equation using integration and initial conditions.

Find the particular solution of $\frac{dy}{dx} = (x^{2}+1)y$ satisfying $y(0)=3$ .

[4]

Question 11

Find the particular solution of $\frac{dy}{dx} = \frac{2x}{3y^{2}}$ satisfying $y(1)=2$ .

[5]

Question 12

Find the particular solution of the differential equation $\frac{dy}{dx} = \frac{x}{y}$ , satisfying the initial condition $y(0) = 3$ .

[4]

Question Type 2: Separating a differential equation into two variables Exercises