Advertisements
Advertisements
Question
`(dy)/(dx)+ y tan x = x^n cos x, n ne− 1`
Advertisements
Solution
We have,
`(dy)/(dx)+ y tan x = x^n cos x`
\[\text{Comparing with }\frac{dy}{dx} + Py = Q,\text{ we get}\]
\[P = \tan x \]
\[Q = x^n \cos x\]
Now,
\[I . F . = e^{\int\tan x dx} \]
\[ = e^{\log\left( sec x \right)} \]
\[ = \sec x\]
So, the solution is given by
\[y \times I . F . = \int Q \times I . F . dx + C\]
\[ \Rightarrow y \sec x = \int x^n \cos x \sec x\ dx + C\]
\[ \Rightarrow y \sec x = \int x^n dx + C\]
\[ \Rightarrow y \sec x = \frac{x^{n + 1}}{n + 1} + C\]
APPEARS IN
RELATED QUESTIONS
Solve the differential equation: `x+ydy/dx=sec(x^2+y^2)` Also find the particular solution if x = y = 0.
Find the particular solution of differential equation:
`dy/dx=-(x+ycosx)/(1+sinx) " given that " y= 1 " when "x = 0`
Find the particular solution of the differential equation x (1 + y2) dx – y (1 + x2) dy = 0, given that y = 1 when x = 0.
Solve the differential equation `cos^2 x dy/dx` + y = tan x
Find the particular solution of the differential equation
`tan x * (dy)/(dx) = 2x tan x + x^2 - y`; `(tan x != 0)` given that y = 0 when `x = pi/2`
Find the differential equation of the family of concentric circles `x^2 + y^2 = a^2`
Solution of the differential equation \[\frac{dy}{dx} + \frac{y}{x}=\sin x\] is
The solution of the differential equation \[2x\frac{dy}{dx} - y = 3\] represents
The solution of the differential equation \[\frac{dy}{dx} + 1 = e^{x + y}\], is
The solution of the differential equation x dx + y dy = x2 y dy − y2 x dx, 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 \[\frac{dy}{dx} = e^{x + y}\], is
The general solution of the differential equation \[\frac{y dx - x dy}{y} = 0\], is
`(2ax+x^2)(dy)/(dx)=a^2+2ax`
x2 dy + (x2 − xy + y2) dx = 0
\[\frac{dy}{dx} + 2y = \sin 3x\]
\[\frac{dy}{dx} + y = 4x\]
Solve the differential equation:
(1 + y2) dx = (tan−1 y − x) dy
For the following differential equation, find the general solution:- \[\frac{dy}{dx} = \sin^{- 1} x\]
Solve the following differential equation:-
\[x\frac{dy}{dx} + 2y = x^2 \log x\]
Solve the following differential equation:-
(1 + x2) dy + 2xy dx = cot x dx
Find the equation of a curve passing through the point (−2, 3), given that the slope of the tangent to the curve at any point (x, y) is `(2x)/y^2.`
Solve the differential equation : `("x"^2 + 3"xy" + "y"^2)d"x" - "x"^2 d"y" = 0 "given that" "y" = 0 "when" "x" = 1`.
Find the general solution of `"dy"/"dx" + "a"y` = emx
Form the differential equation having y = (sin–1x)2 + Acos–1x + B, where A and B are arbitrary constants, as its general solution.
Solve: `y + "d"/("d"x) (xy) = x(sinx + logx)`
If y = e–x (Acosx + Bsinx), then y is a solution of ______.
The differential equation for y = Acos αx + Bsin αx, where A and B are arbitrary constants is ______.
Integrating factor of `(x"d"y)/("d"x) - y = x^4 - 3x` is ______.
y = aemx+ be–mx satisfies which of the following differential equation?
The solution of the differential equation cosx siny dx + sinx cosy dy = 0 is ______.
The solution of the differential equation `("d"y)/("d"x) = (x + 2y)/x` is x + y = kx2.
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)`.
Find the general solution of the differential equation:
`(dy)/(dx) = (3e^(2x) + 3e^(4x))/(e^x + e^-x)`
The differential equation of all parabolas that have origin as vertex and y-axis as axis of symmetry is ______.
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 ______.
