Consider the following differential equation to be solved by variation of parameters. y" + y = sec (0) tan(0) Find the complementary function of the differential equation. yc(8) - -cos(0)tan (0) + 0 cos (0) — In (cos(0))sin (0) Find the general solution of the differential equation. y(0) = c₁cos (0) + c₂sin (0) — sec (0) + 0 cos (0) + sin(0)In (sec (0)) Need Help? Read It
Consider the following differential equation to be solved by variation of parameters. y" + y = sec (0) tan(0) Find the complementary function of the differential equation. yc(8) - -cos(0)tan (0) + 0 cos (0) — In (cos(0))sin (0) Find the general solution of the differential equation. y(0) = c₁cos (0) + c₂sin (0) — sec (0) + 0 cos (0) + sin(0)In (sec (0)) Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Solving Differential Equations using Variation of Parameters
#### Given Differential Equation
\[ y'' + y = \sec(\theta) \tan(\theta) \]
#### Task
Find the complementary function of the differential equation.
#### Complementary Function
\[ y_c(\theta) = -\cos(\theta) \tan(\theta) + \theta \cos(\theta) - \ln(\cos(\theta)) \sin(\theta) \]
#### Task
Find the general solution of the differential equation.
#### General Solution
\[ y(\theta) = c_1 \cos(\theta) + c_2 \sin(\theta) - \sec(\theta) + \theta \cos(\theta) + \sin(\theta) \ln(\sec(\theta)) \]
*Note: The red crosses next to the equations may indicate that these solutions may have errors or need verification.*
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Transcribed Image Text:### Solving Differential Equations using Variation of Parameters
#### Given Differential Equation
\[ y'' + y = \sec(\theta) \tan(\theta) \]
#### Task
Find the complementary function of the differential equation.
#### Complementary Function
\[ y_c(\theta) = -\cos(\theta) \tan(\theta) + \theta \cos(\theta) - \ln(\cos(\theta)) \sin(\theta) \]
#### Task
Find the general solution of the differential equation.
#### General Solution
\[ y(\theta) = c_1 \cos(\theta) + c_2 \sin(\theta) - \sec(\theta) + \theta \cos(\theta) + \sin(\theta) \ln(\sec(\theta)) \]
*Note: The red crosses next to the equations may indicate that these solutions may have errors or need verification.*
For additional help, you may click the "Read It" button.
#### Buttons and Links
- **Submit Answer**: Button to submit your solution.
- **Read It**: Button for additional help or resources.
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