Download App

DIFFERENTIAL EQUATIONS — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDIFFERENTIAL EQUATIONS2 Marks
Question
In each of the verify that the given function (explicit or implicit) is a solution of the corresponding differential equation:
$\text{y} = \text{Ax} \ :\ \text{xy}' = \text{y} (\text{x} \neq0)$
✓

Answer

Given: y = Ax .....(i)
To prove: y given by eq. (i) is a solution of differential equation $\text{xy}' = \text{y}(\text{x} \neq0)\ ....(\text{ii})$
Proof: From eq. (i) y' = A(1) = A
L.H.S. of eq. (ii) = xy' = xA = Ax = y = R.H.S. of eq. (ii)
$\therefore$ y given by eq. (i) is a solution of differential equation $\text{xy}' = \text{y}(\text{x} \neq 0).$

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 "2 Marks" from DIFFERENTIAL EQUATIONS→DIFFERENTIAL EQUATIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},$ then find $\big(\vec{\text{a}}\times\vec{\text{b}}\big)\vec{\text{a}}.$
→
$\sin^{-1}\Big\{\cos\Big(\sin^{-1}\frac{\sqrt3}{2}\Big)\Big\}$
→
If A is a non-singular square matrix such that |A| = 10, find |A-1|.
→
Prove that : $\tan ^{-1} \sqrt{x}=\frac{1}{2} \cos ^{-1}\left[\frac{1-x}{1+x}\right] ; x \in[0,1] .$
→
Evaluate: $\begin{vmatrix}\cos15^\circ&\sin15^\circ\\\sin75^\circ&\cos75^\circ\end{vmatrix}$
→
Construct a 2 × 3 matrix A = [aij] whose elements aij are give by:
aij = i.j
→
Find the value of x, if:
$\begin{vmatrix}2&4\\5&1\end{vmatrix}=\begin{vmatrix}2\text{x}&4\\6&\text{x}\end{vmatrix}$
→
A fair coin is tossed 8 times, find the probability of.
at most six heads.
→
If the binary operation o is defined by a o b = a + b - ab on the set Q - {-1} of all rational numbers other than 1, shown that o is commutative on Q - [1].
→
Form the differential equation representing the family of curves y = e2x(a + bx), where ‘a’ and ‘b’ are arbitrary constants.
→