Differential Equations in a Day

Students will use the method of separation of variables to solve first order differential equations.

Students will use a substitution method to change the variable and solve the differential equation.

Students will find particular solutions to separable differential equations with a given initial condition.

Check how much you've learnt about Separable Differential Equations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe linear first-order differential equations and describe how they are solved using an integrating factor.

Students will find general solutions to linear first-order differential equations using an integrating factor.

Students will find particular solutions to linear first-order differential equations using an integrating factor where an initial condition has been given.

Check how much you've learnt about Linear First-Order Differential Equations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will describe second-order homogeneous differential equations and the approach to solving them using the characteristic equation.

Students will solve second-order homogeneous differential equations where the characteristic equation has distinct real roots.

Students will solve second-order homogeneous differential equations where the characteristic equation has equal roots.

Students will solve second-order homogeneous differential equations where the characteristic equation has complex roots.

Students will find particular solutions to second-order homogeneous differential equations using an integrating factor where an initial condition has been given.

Check how much you've learnt about Second-Order Homogeneous Differential Equations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will state what second-order non-homogeneous differential equations are and describe the approach to solving them using a complementary function and particular integral.

Students will practise solving second-order non-homogeneous differential equations using the method of undetermined coefficients.

Check how much you've learnt about Second-Order Non-Homogeneous Differential Equations by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will state the Laplace Transform and describe, in general terms, how it might be evaluated for different function types.

Students will evaluate the Laplace Transform of various functions using the definition of the Laplace Transform.

Students will state key properties of the Laplace Transform and situations in which they can be used.

Students will evaluate the Laplace Transform of various functions using known Laplace Transforms.

Check how much you've learnt about Laplace Transforms by trying these practice questions. Remember to check your work against the step by step solutions provided.

Students will evaluate inverse Laplace transforms using the table of Laplace transforms.

Students will evaluate inverse Laplace transforms using transforms of integrals.

Students will describe the Laplace transform of the derivative of a function and develop a method for subsequent derivatives.

Students will solve initial value differential equation problems using Laplace transforms.

Check how much you've learnt about Methods of Laplace Transforms by trying these practice questions. Remember to check your work against the step by step solutions provided.

Formula list for the Differential Equations in a Day course.

Table of Laplace Transforms.