Advertisements
Advertisements
प्रश्न
Solve the differential equation:
`dy/dx = 1 +x+ y + xy`
उत्तर
`dy/dx =1 + x+ y +xy`
=(1 + x)+ y (1+x)
= (1 + x) (1 + y)
∴ `dy/(1+y) = (1+x) dx`
Integrating on both sides, we get
`intdy/(1+y) =int (1+x) dx`
∴ `log | 1+y| = x + x^2/2 + c`
APPEARS IN
संबंधित प्रश्न
For the differential equation, find the general solution:
`dy/dx = (1 - cos x)/(1+cos x)`
For the differential equation, find the general solution:
`dy/dx = sqrt(4-y^2) (-2 < y < 2)`
For the differential equation, find the general solution:
sec2 x tan y dx + sec2 y tan x dy = 0
For the differential equation, find the general solution:
`dy/dx = sin^(-1) x`
For the differential equation find a particular solution satisfying the given condition:
`cos (dx/dy) = a(a in R); y = 1` when x = 0
Find the equation of a curve passing through the point (0, -2) given that at any point (x, y) on the curve, the product of the slope of its tangent and y-coordinate of the point is equal to the x-coordinate of the point.
The volume of spherical balloon being inflated changes at a constant rate. If initially its radius is 3 units and after 3 seconds it is 6 units. Find the radius of balloon after t seconds.
In a bank, principal increases continuously at the rate of r% per year. Find the value of r if Rs 100 doubles itself in 10 years (loge 2 = 0.6931).
Find the particular solution of the differential equation `dy/dx + 2y tan x = sin x` given that y = 0 when x = `pi/3`
Solve the equation for x:
sin-1x + sin-1(1 - x) = cos-1x, x ≠ 0
Solve `dy/dx = (x+y+1)/(x+y-1) when x = 2/3 and y = 1/3`
Solve
y dx – x dy = −log x dx
The resale value of a machine decreases over a 10 year period at a rate that depends on the age of the machine. When the machine is x years old, the rate at which its value is changing is ₹ 2200 (x − 10) per year. Express the value of the machine as a function of its age and initial value. If the machine was originally worth ₹1,20,000, how much will it be worth when it is 10 years old?
Solve
`y log y dx/ dy = log y – x`
Find the solution of `"dy"/"dx"` = 2y–x.
Solve the differential equation `(x^2 - 1) "dy"/"dx" + 2xy = 1/(x^2 - 1)`.
Solve the differential equation `"dy"/"dx" + 1` = ex + y.
Polio drops are delivered to 50 K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of 2nd week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `"dy"/"dx" = "k"(50 - "y")` where x denotes the number of weeks and y the number of children who have been given the drops.
Which method of solving a differential equation can be used to solve `"dy"/"dx" = "k"(50 - "y")`?
