Advertisements
Advertisements
Question
Solve: `("d"y)/("d"x) = y sin 2x`
Advertisements
Solution
`("d"y)/("d"x) = y sin 2x`
⇒ `("d"y)/y = sin 2x "d"x`
Integrating on both sides
`int 1/y "d"y = int sin 2x "d"x`
⇒ log y = `(- cos 2x)/2 + "c"`
APPEARS IN
RELATED QUESTIONS
The velocity v, of a parachute falling vertically satisfies the equation `"v" (dv)/(dx) = "g"(1 - v^2/k^2)` where g and k are constants. If v and are both initially zero, find v in terms of x
Solve the following differential equation:
`x ("d"y)/("d"x) = y - xcos^2(y/x)`
Solve: `log(("d"y)/("d"x))` = ax + by
Solve the following homogeneous differential equation:
`x ("d"y)/("d"x) = x + y`
Solve the following:
`("d"y)/(""dx) + y cos x = sin x cos x`
Solve the following:
A bank pays interest by continuous compounding, that is by treating the interest rate as the instantaneous rate of change of principal. A man invests ₹ 1,00,000 in the bank deposit which accrues interest, 8% per year compounded continuously. How much will he get after 10 years? (e0.8 = 2.2255)
Choose the correct alternative:
The integrating factor of the differential equation `("d"y)/("d"x) + "P"x` = Q is
Choose the correct alternative:
If sec2 x is an integrating factor of the differential equation `("d"y)/("d"x) + "P"y` = Q then P =
Choose the correct alternative:
A homogeneous differential equation of the form `("d"x)/("d"y) = f(x/y)` can be solved by making substitution
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (f(y/x))/(f"'"(y/x))` is
