Can R language find a generic solution of the first order differential equation?

Question

Can R language find a generic solution of the first order differential equation?

For example:

(5x-6)^2 y' = 5(5x-6) y - 2 

PS:
That can be easily solved by hand, i.e. particular solution is:

y = 1/(5(5x-6))

and generic

C*(5x-6)

I need to understand whether R can do it?

Answer 1

We can use the R library deSolve to obtain numerical solutions of ODEs. See ?deSolve for details.

Here is a worked-through example based on your ODE.

1. Load the R library

   library(deSolve);
   

2. Define the differential equation

   # Define the function
   f <- function(x, y, params) list((5 * (5 * x - 6) * y - 2) / (5 * x - 6)^2)
   

3. Set x values for which to solve and initial condition

   # x values for which to solve
   x <- seq(2, 10, length.out = 100);
   
   # Initial value y(x=2) = 1/20
   y0 <- 1/20
   

4. Solve the ODE

   # Solve ODE
   df <- as.data.frame(ode(y0, x, f, parms = NULL));
   

5. Plot theoretical (algebraic) solution and numerical solution from deSolve

   # Plot
   library(ggplot2);
   ggplot(df, aes(time, `1`)) +
       stat_function(
           fun = function(x) 1/(5 * (5 * x - 6)),
           aes(colour = "Theoretical"),
           size = 4) +
       geom_line(aes(colour = "deSolve"), size = 2) +
       labs(x = "x", y = "y")