Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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![**Solving First-Order Differential Equations**
We are given the following ordinary differential equation (ODE):
\[
\left( 3x^2 - 10xy + 5 \right) + \left( 15y^2 - 5x^2 - 2 \right) y' = 0
\]
**Entry Format:**
Write your solution equation so that:
1. The equation is in implicit form.
2. The highest degree term containing only \( x \) has a coefficient of 1.
3. Constants are combined and moved to the right-hand side (RHS) of the equation.
Below this instructional text, there is a blank field for entering the solution:
\[
\quad \quad \quad \quad \quad\quad\quad\quad\quad\quad\quad = C
\]
where \( C \) denotes the constant of integration.
**Note for the Learner:**
When solving differential equations:
- Put your final answer in the implicit form as required.
- Simplify your answer so that the coefficient of the highest degree term of \( x \) is 1.
- Move all constant terms to the right-hand side of the equation to satisfy the conditions given.
Insert your completed solution in the box, equating the left-hand side expression to the constant \( C \).](https://content.bartleby.com/qna-images/question/b91fc3bc-dc3a-458d-9c8d-88d0ab085f00/4caf3507-f43e-48a5-b1ba-6586b539dc98/lri32bg_processed.jpeg)
Transcribed Image Text:**Solving First-Order Differential Equations**
We are given the following ordinary differential equation (ODE):
\[
\left( 3x^2 - 10xy + 5 \right) + \left( 15y^2 - 5x^2 - 2 \right) y' = 0
\]
**Entry Format:**
Write your solution equation so that:
1. The equation is in implicit form.
2. The highest degree term containing only \( x \) has a coefficient of 1.
3. Constants are combined and moved to the right-hand side (RHS) of the equation.
Below this instructional text, there is a blank field for entering the solution:
\[
\quad \quad \quad \quad \quad\quad\quad\quad\quad\quad\quad = C
\]
where \( C \) denotes the constant of integration.
**Note for the Learner:**
When solving differential equations:
- Put your final answer in the implicit form as required.
- Simplify your answer so that the coefficient of the highest degree term of \( x \) is 1.
- Move all constant terms to the right-hand side of the equation to satisfy the conditions given.
Insert your completed solution in the box, equating the left-hand side expression to the constant \( C \).
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