Advertisements
Advertisements
प्रश्न
Solve: `("d"y)/("d"x) + "e"^x + y"e"^x = 0`
Advertisements
उत्तर
`("d"y)/("d"x) + "e"^x + y"e"^x = 0`
`("d"y)/("d"x) = - y"e"^x - "e"^x`
`("d"y)/("d"x) = - "e"^x (y + 1)`
`1/((y + 1)) "d"y = - "e"^x "d"x`
Integrating on both sides
`int 1/((y + 1)) "d"x = - int "e"^x "d"x`
⇒ log (y + 1) = `- "e"^x + "c"`
APPEARS IN
संबंधित प्रश्न
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 cos y dy = ex(x log x + 1) dx
Choose the correct alternative:
The solution of the differential equation `("d"y)/("d"x) = y/x + (∅(y/x))/(∅(y/x))` is
Choose the correct alternative:
The number of arbitrary constants in the general solutions of order n and n +1are respectively
Solve: `("d"y)/("d"x) = "ae"^y`
Solve the following homogeneous differential equation:
(y2 – 2xy) dx = (x2 – 2xy) dy
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 solution of the differential equation `("d"y)/("d"x) + "P"y` = Q where P and Q are the function of x is
Form the differential equation having for its general solution y = ax2 + bx
Solve x2ydx – (x3 + y3) dy = 0
