1. Advance Engineering Mathematics – 2130002 Active Learning Assignment Topic: First ODE(Integrating Factor to Orthogonal trajectories of curves) First ODE(Integrating Factor to Orthogonal trajectories of curves) Branch : Mechanical Engineering

2. Presented by : Nilesh H. Patel(130460119107) Harsh V. Patel(130460119098) Akshay V. Patel(130460119080) Neel D. Patel(130460119106) Guided by : Prof. Hemlata Pandey

3. First Order Differential Equation Differential equation may be defined as equation which involves differentials or differential co- efficient. The variable from which these differentials or differential coefficients may or may not occur in the differential equation. First order differential equation involve only the first derivative of the unknown function and no higher derivatives.

4. Types of First Order Differential Equations 1. 1.Variable Separable Equation 2. 2.Homogeneous Differential Equation 3. 3.Exact Differential Equation 4. 4. Linear Differential Equation 5. 5. Bernoulli’s Equation In this Presentation

5. Linear Differential Equation A Differential Equation in which dependent variable and its derivatives occur only in first degree and both are not multiplied together is called a Linear Differential Equation.

11. APPLICATION OF FIRST ORDER DIFFERENTIAL EQUATION

12. ORTHOGONAL TRAJECTORIES A curve which cuts every member of a family of curves according to some specified property is called a trajectory of the given family of curves. A curve which cuts every member of a family of curves according to some specified property is called a trajectory of the given family of curves. A curve that intersects every member of a one parameter family of curves orthogonally ( at right angles) is called an orthogonal trajectory of the given family of curves. A curve that intersects every member of a one parameter family of curves orthogonally ( at right angles) is called an orthogonal trajectory of the given family of curves.

13. HOW TO FIND ORTHOGONAL TRAJECTORIES?

17. EXAMPLE(2): FIND ORTHOGONAL TRAJECTORIES OF XY=C