Question
What is integrating factor of $\frac{d y}{d z}+y \sec x=\tan x$ ?
✓
Answer
(c) $\sec x+\tan x$
Explanation: We have,
$
\frac{d y}{d x}+y \sec x=\tan x
$
Comparing with $\frac{d y}{d x}+ Py = Q$
$
=\sec x, Q=\tan x
$
I. $F \cdot=e^{\int \sec x d x}=e^{\log (\sec x+\tan x)}=\sec x+\tan x$
Explanation: We have,
$
\frac{d y}{d x}+y \sec x=\tan x
$
Comparing with $\frac{d y}{d x}+ Py = Q$
$
=\sec x, Q=\tan x
$
I. $F \cdot=e^{\int \sec x d x}=e^{\log (\sec x+\tan x)}=\sec x+\tan x$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Derivative of $e^{2 x}$ with respect to $e^x$, is
→If the x-coordinate of a point P on the join of Q(2, 2, 1) and R(5, 1, -2) is 4, then its z-coordinate is:
- 2
- 1
- -1
- -2
The angle of intersection of the curves $xy = a^2$ and $x^2 - y^2 = 2a^{2 }$ is:
→$\int\frac{\cos2\text{x dx}}{(\sin\text{x}+\cos\text{x})^2}=$
→- $-\frac{1}{\sin\text{x}+\cos\text{x}}+\text{c}$
- $\log|\sin\text{x}+\cos\text{x }|+\text{c}$
- $\log|\sin\text{x}-\cos\text{x }|+\text{c}$
- $\frac{1}{(\sin\text{x}+\cos\text{x})^2}$
If $A$ and $B$ are symmetric matrices of the same order, then
→Corner points of the feasible region determined by the system of linear constraints are (0, 3), (1, 1) and (3, 0). Let Z = px + qy, where p, q > 0. Condition on p and q so that the minimum of Z occurs at (3, 0) and (1, 1) is:
→- $\text{p}=2\text{q}$
- $\text{p}=\frac{\text{q}}{2}$
- $\text{p}=3\text{q}$
- $\text{p}=\text{q}$
Let $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then f(f(x)) is:
→- $\frac{1}{\text{x}}$
- $-\frac{1}{\text{x}}$
- $\frac{1}{\text{x}+1}$
- $\frac{1}{\text{x}-1}$
Degree of the differential equation $\sin x+\cos \left(\frac{d y}{d x}\right)=y^2$ is
→Which of the following is an essential condition in a situation for linear programming to be useful?
Shown below is the curve defined by the equation $y=\log (x+1)$ for $x \geq 0$.
Which of these is the area of the shaded region?
→Which of these is the area of the shaded region?