Download App

Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations1 Mark
MCQ
The general solution of the differntial equation $\frac{\text{dy}}{\text{dx}}+\text{y}\cot\text{x}=\text{coses}\ \text{x}$ is:
  • A
    $\text{x}+\text{y}\sin\text{x}=\text{C}$
  • B
    $\text{x}+\text{y}\cos\text{x}=\text{C}$
  • C
    $\text{y}+\text{x}(\sin\text{x}+\cos\text{x})=\text{C}$
  • ✓
    $\text{y}\sin\text{x}=\text{x}+\text{C}$
✓

Answer

Correct option: D.
$\text{y}\sin\text{x}=\text{x}+\text{C}$
$\frac{\text{dy}}{\text{dx}}+\text{y}\cot\text{x}=\text{coses}\ \text{x}$
Comparting with $\frac{\text{dy}}{\text{dx}}+\text{Py}=\text{Q}$ we get
$\text{P}=\cot\text{x}$
$\text{Q}=\text{coses} \ \text{x}$
Now,
$\text{I.F}=\text{e}^{\int\cot\text{x}\text{dx}}$
$=\text{e}^{\log(\sin\text{x})}$
$=\sin\text{x}$
So, the solution is given by
$\Rightarrow \text{y}\sin\text{x}=\int\sin\text{x}\times\text{cosec}\ \text{x}\text{dx}+\text{C}$
$\Rightarrow \text{y}\sin\text{x}=\text{x}+\text{C}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\int\frac{\sin\text{x}}{3+4\cos^2\text{x}}\text{ dx}=$
→
Which of the following statements is a tautology?
→
Area bounded by the curve $x y= c , X$-axis between $x=1, x=4$ is
→
If $\int_0^a\left(3 x^2+2 x+1\right) d x=14$, then $\alpha=\ldots .$.
→
If $\vec{\text{a}}$ and $\vec{\text{b}}$ be two unit vectors and $\theta$ the angle between them, than $\vec{\text{a}}+\vec{\text{b}}$ is a unit vector if $\theta=$
→
The dual of $'(p \wedge t) \vee(c \wedge \sim q)^{\prime}$ where t is a V tautology and c is a contradiction, is
→
General solution of the equation $\tan \theta \tan 2 \theta=1$ is given by
→
The points with position vectors $20 \hat{ i }+ p \hat{ j }$, $5 \hat{i}-\hat{j}$ and $10 \hat{i}-13 \hat{j}$ are collinear. The value of $p$ is
→
Which of the following functions from $\text{A}=\{\text{x}:-1\leq\text{x}\leq1\}$ to itself are bijections?
→
Equation of a plane passing through $(1,1,1)$ and containing $X$-axis is
→