Verify that y = –x – 1 is a solution of the differential equation (y – x)dy – (y2 – x2)dx = 0.
The differential equation is and the function to be proven as the solution is
y = – x – 1, now we need to find the value of .
= –1
Putting the values in equation,
–1 = –x –1 +x
As, L.H.S = R.H.S. the equation is satisfied, so hence this function is the solution of the differential equation.