Reference no: EM133052196
Learning Outcome 1: Describe the basic concepts of differential equations and solve equations containing arbitrary constants;
Learning Outcome 2: Solve solutions of first - order differential equations using an appropriate method;
Learning Outcome 3: Solve solutions of more complex differential equations using integrating factors and appropriate substitution methods;
Learning Outcome 4: Apply first - order differential equation for predicting the behavior of the system defined;
Learning Outcome 5: Solve the solution of higher - order differential equations using the most appropriate method; and
Learning Outcome 6: Solve Laplace Transformation problems to obtain solutions of differential equations.
This aims to give you an overview of more complex differential equations. It will enable you to analyze the equation, and use integrating factors and substitution methods to obtain the solution of a differential equation using the most appropriate method.
Recall your learnings from the previous module. Answer the following questions by writing your answers in the space provided.
1. When is separation of variables applicable?
2. How can homogeneous equations be distinguished?
3. When is the exact method applicable?
4. Why is there a need to solve for integrating factors?
1. y dx + (x + x3y2)dy = 0
2. y(x3 - y)dx - x(x3 + y)dy = 0
3. (4xy + 3y2 - x)dx + x(x + 2y)dy = 0
4. y(x + y + 1)dx + x(x + 2y + 2)dy = 0
5. (x + 2y - 1)dx + 3(x + 2y)dy = 0
6. (1 + 3x sin y)dx - x2 cosy dy = 0
7. (x + 2y - 4)dx - (2x + y - 5)dy = 0
8. (2x + 3y - 1)dx + (2x + 3y + 2)dy = 0
9. y(6y2 - x - 1)dx + 2xdy = 0
10. 6y2 dx - x(2x3 + y)dy = 0