Question:
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
Complete integral of the partial differential equation \( 2\frac{\partial^2 f}{\partial q^2} + 3\frac{\partial f}{\partial q} = 6x + 2y \) is
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When solving partial differential equations, use the method of characteristics to find the general solution and ensure to account for all constants.
Updated On: May 5, 2025
- \( z = \frac{1}{12}(6x + a)^2 + \frac{1}{54}(2y - a)^3 + b \)
- \( z = \frac{1}{72}(6x - a)^3 + \frac{1}{54}(2y - a)^3 + b \)
- \( z = \frac{1}{12}(6x - a)^2 + \frac{1}{72}(2y - a)^3 + b \)
- \( z = \frac{1}{54}(6x - a)^3 + \frac{1}{12}(2y - a)^3 + b \)
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Solution and Explanation
The complete integral of the given partial differential equation is derived by solving for the general solution and using the method of characteristics. The result is given by \( z = \frac{1}{12}(6x + a)^2 + \frac{1}{54}(2y - a)^3 + b \).
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