1. Differential Equations Verification Examples Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

2. Verify that the given function satisfies the differential equation. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

3. Verify that the given function satisfies the differential equation. First compute the derivative: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

4. Verify that the given function satisfies the differential equation. First compute the derivative: Now substitute into the differential equation: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

5. Verify that the given function satisfies the differential equation. First compute the derivative: Now substitute into the differential equation:  This is true, so the equation is satisfied Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

6. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

7. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

8. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Substitute into diff. eq.: Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

9. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Substitute into diff. eq.:  This is true, so the equation is satisfied Now we need to satisfy the initial condition. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

10. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Substitute into diff. eq.:  This is true, so the equation is satisfied Now we need to satisfy the initial condition. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

11. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Substitute into diff. eq.:  This is true, so the equation is satisfied Now we need to satisfy the initial condition. Set this equal to -1 Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB

12. Verify that the given function satisfies the differential equation, and find a value for C that satisfies the given initial condition. Find the derivative: Substitute into diff. eq.:  This is true, so the equation is satisfied Now we need to satisfy the initial condition. Set this equal to -1 Our final solution is thus We will call this a particular solution because it matches with a particular initial condition. Prepared by Vince Zaccone For Campus Learning Assistance Services at UCSB