Question

Solve the ODE: (3x²+6xy+4)+(15y²+3x²-5) 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 RHS of the equation.

Answer 1

To solve the given ODE, rearrange the equation and set it equal to zero. The solution equation is in implicit form with the highest degree term containing only x having a coefficient of 1, and the constants moved to the RHS.

Step-by-step explanation:

To solve the given ordinary differential equation (ODE):

(3x²+6xy+4)+(15y²+3x²-5) y′=0,

we can rearrange the equation by combining like terms to get:

(6x²+6xy+15y²-1) y′=0.

To find the solution, we set the equation equal to zero:

6x²+6xy+15y²-1 = 0.

Now, we have an implicit equation in the required form. The highest degree term containing only x has a coefficient of 1, and the constants are combined and moved to the right-hand side (RHS) of the equation.