A Note Order and degree (if defined) of a differential equation are always · Part 5

the differential equation , ( y ≠ ) Solution We have Separating the variables in equation ( ), we get ( – y ) dy = ( x + ) dx Integrating both sides of equation ( ), we get ( y dy ) y − x + y + x – y + C = x + y + x – y + C = , where C = 2C which is the general solution of equation ( ). Example Find the general solution of the differential equation Solution Since + y ≠ , therefore separating the variables, the given differential equation can be written as Integrating both sides of equation ( ), we get tan – y = tan – x + C which is the general solution of equation ( ). Example Find the particular solution of the differential equation dx = − given that y = , when x = . Solution If y ≠ , the given differential equation can be written as y = – x dx Integrating both sides of equation ( ), we get