Advertisements
Advertisements
प्रश्न
Solve the differential equation `dy/dx -y =e^x`
उत्तर
`dy/dx -y =e^x`
The given equation is of the form `dy/dx+Py=Q`
Where, `P=-1 and Q=e^x`
`I.F=e^(intpdx)=e^(int-1dx)=e^-x`
Solution of the given equation is
`y(I.F)=intQ(I.F) dx +c`
`y.e^-x=inte^x.e^-xdx+c`
`ye^-x=x+c`
we get c = 1
`y.e^(-x)=x+1`
`y = (x + 1) e^x` is a particular solution of D.E.
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.
Form the differential equation of the family of circles in the second quadrant and touching the coordinate axes.
Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, 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 y = x : (y sin y + cos y + x) y′ = y
Verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
x + y = tan–1y : y2 y′ + y2 + 1 = 0
The number of arbitrary constants in the particular solution of a differential equation of third order are ______.
The general solution of the differential equation \[\frac{dy}{dx} + y \] cot x = cosec x, is
The solution of the differential equation (x2 + 1) \[\frac{dy}{dx}\] + (y2 + 1) = 0, is
The solution of the differential equation \[\frac{dy}{dx} = \frac{x^2 + xy + y^2}{x^2}\], is
The number of arbitrary constants in the general solution of differential equation of fourth order is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
The general solution of a differential equation of the type \[\frac{dx}{dy} + P_1 x = Q_1\] is
x (e2y − 1) dy + (x2 − 1) ey dx = 0
\[\frac{dy}{dx} + 1 = e^{x + y}\]
\[\frac{dy}{dx} + \frac{y}{x} = \frac{y^2}{x^2}\]
(1 + y + x2 y) dx + (x + x3) dy = 0
(x3 − 2y3) dx + 3x2 y dy = 0
\[x\frac{dy}{dx} + x \cos^2 \left( \frac{y}{x} \right) = y\]
For the following differential equation, find the general solution:- \[\frac{dy}{dx} + y = 1\]
Solve the following differential equation:- \[x \cos\left( \frac{y}{x} \right)\frac{dy}{dx} = y \cos\left( \frac{y}{x} \right) + x\]
Solve the following differential equation:-
\[\frac{dy}{dx} - y = \cos x\]
Solve the following differential equation:-
\[\frac{dy}{dx} + 3y = e^{- 2x}\]
The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.
y = x is a particular solution of the differential equation `("d"^2y)/("d"x^2) - x^2 "dy"/"dx" + xy` = x.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Find the general solution of `(x + 2y^3) "dy"/"dx"` = y
Solve the differential equation (1 + y2) tan–1xdx + 2y(1 + x2)dy = 0.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
Integrating factor of the differential equation `cosx ("d"y)/("d"x) + ysinx` = 1 is ______.
tan–1x + tan–1y = c is the general solution of the differential equation ______.
Integrating factor of the differential equation `("d"y)/("d"x) + y tanx - secx` = 0 is ______.
The general solution of the differential equation `("d"y)/("d"x) = "e"^(x^2/2) + xy` is ______.
The solution of the differential equation `x(dy)/("d"x) + 2y = x^2` is ______.
Number of arbitrary constants in the particular solution of a differential equation of order two is two.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
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.
The value of c in the particular solution given that y(0) = 0 and k = 0.049 is ______.
The curve passing through (0, 1) and satisfying `sin(dy/dx) = 1/2` is ______.
