Advertisements
Advertisements
प्रश्न
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
पर्याय
\[y e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
\[y e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
Advertisements
उत्तर
\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
We have,
\[\frac{dx}{dy} + P_1 x = Q_1\]
Comparing with the equation \[\frac{dx}{dy} + Px = Q\], we get
P = P1
Q = Q1
The general solution of the equation \[\frac{dx}{dy} + Px = Q\] is given by \[x e^{\int Pdy} = \int\left\{ Q e^{\int Pdy} \right\}dy + C\] ...(1)
Putting the value of P and Q in (1), we get
\[x e^{\int P_1 dy} = \int\left\{ Q_1 e^{\int P_1 dy} \right\}dy + C\]
APPEARS IN
संबंधित प्रश्न
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
The differential equation of the family of curves y=c1ex+c2e-x is......
(a)`(d^2y)/dx^2+y=0`
(b)`(d^2y)/dx^2-y=0`
(c)`(d^2y)/dx^2+1=0`
(d)`(d^2y)/dx^2-1=0`
Solve : 3ex tanydx + (1 +ex) sec2 ydy = 0
Also, find the particular solution when x = 0 and y = π.
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the general solution of the following differential equation :
`(1+y^2)+(x-e^(tan^(-1)y))dy/dx= 0`
Find the particular solution of the differential equation `dy/dx=(xy)/(x^2+y^2)` given that y = 1, when x = 0.
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
y = cos x + C : y′ + sin x = 0
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
`y sqrt(1 + x^2) : y' = (xy)/(1+x^2)`
Find the general solution of the differential equation `dy/dx + sqrt((1-y^2)/(1-x^2)) = 0.`
Show that the general solution of the differential equation `dy/dx + (y^2 + y +1)/(x^2 + x + 1) = 0` is given by (x + y + 1) = A (1 - x - y - 2xy), where A is parameter.
The population of a town grows at the rate of 10% per year. Using differential equation, find how long will it take for the population to grow 4 times.
The solution of the differential equation \[\frac{dy}{dx} = 1 + x + y^2 + x y^2 , y\left( 0 \right) = 0\] is
The solution of the differential equation \[x\frac{dy}{dx} = y + x \tan\frac{y}{x}\], is
If m and n are the order and degree of the differential equation \[\left( y_2 \right)^5 + \frac{4 \left( y_2 \right)^3}{y_3} + y_3 = x^2 - 1\], then
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
Which of the following differential equations has y = x as one of its particular solution?
The general solution of the differential equation \[\frac{dy}{dx} = e^{x + y}\], is
Find the particular solution of the differential equation `(1+y^2)+(x-e^(tan-1 )y)dy/dx=` given that y = 0 when x = 1.
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
Solve the following differential equation:-
\[\frac{dy}{dx} + \left( \sec x \right) y = \tan x\]
Solve the following differential equation:-
\[\left( x + 3 y^2 \right)\frac{dy}{dx} = y\]
Find the equation of a curve passing through the point (0, 0) and whose differential equation is \[\frac{dy}{dx} = e^x \sin x.\]
Find the differential equation of all non-horizontal lines in a plane.
The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
Find the general solution of the differential equation `(1 + y^2) + (x - "e"^(tan - 1y)) "dy"/"dx"` = 0.
Solve:
`2(y + 3) - xy (dy)/(dx)` = 0, given that y(1) = – 2.
Solution of `("d"y)/("d"x) - y` = 1, y(0) = 1 is given by ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The solution of the differential equation `("d"y)/("d"x) + (1 + y^2)/(1 + x^2)` is ______.
The solution of `("d"y)/("d"x) + y = "e"^-x`, y(0) = 0 is ______.
The general solution of the differential equation (ex + 1) ydy = (y + 1) exdx is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
Find the particular solution of the differential equation `x (dy)/(dx) - y = x^2.e^x`, given y(1) = 0.
Find the general solution of the differential equation `x (dy)/(dx) = y(logy - logx + 1)`.
If the solution curve of the differential equation `(dy)/(dx) = (x + y - 2)/(x - y)` passes through the point (2, 1) and (k + 1, 2), k > 0, then ______.
