Further Problems on Separation of variables, implicit/explicit solutions (8) A s
ID: 2878442 • Letter: F
Question
Further Problems on Separation of variables, implicit/explicit solutions (8) A simple first order ODE with an independent variable x is given as: y =y Show by method of separation of variable that a solution is obtainable with A = ec where c is an arbitrary constant. (Hint: Your solution step should not be more than 4 or 5 lines) (9) Solve following problems using method of separation of variables. Is the appropriate solution that you selected implicit or explicit? 2 dy dx (iv) y' = y2 ln (ty) 11) 1 = 2iExplanation / Answer
8. y' = y
=> dy/dx = y
=> dy/y = dx
on integrating both sides
=> ln y = x + c [where c is a constant]
=> y= A.ex [ A = ec ]
9. (i) y' = x2/y
=> ydy = x2dx
On integrating both sides
=> y2/2 = x3/3 + c
Explicit
(ii) i' = (1+2t)/2i
=> di/dt = (1+2t)/2i
=> 2i di = (1+2t) dt
On integrating both sides
=> i2 = t + t2 + c
Explicit
(iii) dy/dx = x / (1+y2)
=> (1+y2) dy = x dx
On integrating both sides
=> y + y3/3 = x2/2 + c
Explicit
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