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
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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 \( C \).
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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