Implement a Physics$-$Informed Neural Network $($PINN$)$ to solve the

differential equation:

y $=2$xy $,$ y $(1)=1$

Compare the predicted solution to the exact solution y $($x$)=$ ex$21.$

Set up the neural network with x as input and y $($x$)$ as output.

$2$ Define the loss function that includes the equation residual and

boundary condition.

$3$ Train the model on the domain x in $[1,1\mathrm{.}5].$

$4$ Compare the predicted values with the exact solution.