Download App

DIFFERENTIAL EQUATIONS — MATHS STD 12 Science — Question

Rajasthan BoardEnglish MediumSTD 12 ScienceMATHSDIFFERENTIAL EQUATIONS3 Marks
Question
Differential equation $\text{x}\frac{\text{dy}}{\text{dx}}=1,\text{y}(1)=0$Function $\text{y}=\log\text{x}$
✓

Answer

Here, y = logxDifferentiating it with respect to x,
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$
$\text{x}\frac{\text{dy}}{\text{dx}}=1$
so, y=logx is a solution of the equation
If $\text{x}=1,\text{y}=\log1=0$
so,
y(1) = 0

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 "3 Marks Question" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=\text{x}^{\frac{2}{3}}\text{ on }[-1,1]$
→
Find the value of $\lambda$ so that the following vectors are coplanar:
$\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}},\vec{\text{b}}=3\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}},\vec{\text{c}}=\hat{\text{i}}+2\hat{\text{j}}+2\hat{\text{k}}$
→
Find the value of k for which $\text{f(x)}=\begin{cases}\frac{1-\cos4\text{x}}{8\text{x}^2},&\text{when x}\neq0\\\text{k},&\text{when x}=0\end{cases}$ is continous at x = 0.
→
Check whether the relation R defined on the set A = {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1} is reflexive, symmetric or transitive.
→
Write the value of $\cos^{-1}\Big(\frac{1}{2}\Big)+2\sin^{-1}\Big(\frac{1}{2}\Big).$
→
Write the set of values of k for which $\text{f}(\text{x})=\text{k}\text{x}-\sin\text{x}$ is increasing on R.
→
If A, B, C, D are the points with position vectors $\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},\ 2\hat{\text{i}}-\hat{\text{j}}+3\hat{\text{k}},\ 2\hat{\text{i}}-3\hat{\text{k}},$ respectively, find the projection of $\overrightarrow{\text{AB}}$ along $\overrightarrow{\text{CD}}.$
→
Examine the continuity of function.$
f(x)=\left\{\begin{array}{ll}
1+x, & x \leq 3 \\
7-x, & x>3
\end{array} \text { at } x=3\right.
$
→
If $x^2+y^2=t-\frac{1}{t}$ and $x^4+y^4=t^2+\frac{1}{t^2}$, then prove that $x \frac{d^2 y}{d x^2}+2 \frac{d y}{d x}=0$
→
For the principal values, evaluate the following:
$\sin^{-1}[\cos\{2\text{cosec}^{-1}(-2)\}]$
→