Solve the ODE: (3r? – 10ry + 5) + (15y? – 5a? – 2)y' = 0 Entry format: Write your solution equation so that: (1) The equation is in implicit form. (2) The highest degree term containing only z has a coefficient of 1. (3) Constants are combined and moved to the RHS of the equation. = C
Solve the ODE: (3r? – 10ry + 5) + (15y? – 5a? – 2)y' = 0 Entry format: Write your solution equation so that: (1) The equation is in implicit form. (2) The highest degree term containing only z has a coefficient of 1. (3) Constants are combined and moved to the RHS of the equation. = C
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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Rate of Change
The relation between two quantities which displays how much greater one quantity is than another is called ratio.
Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![**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 \( C \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb91fc3bc-dc3a-458d-9c8d-88d0ab085f00%2F4caf3507-f43e-48a5-b1ba-6586b539dc98%2Flri32bg_processed.jpeg&w=3840&q=75)
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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