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:
$\text{y} = \text{x}^2 + 2\text{x} +\text{C}\ :\ \text{y}' – 2\text{x} – 2 = 0$
✓

Answer

Given: $y = x^2 + 2x + C .....(i)$
To prove: y is a solution of the differential equation $y' - 2x - 2 = 0 .....(ii)$
Proof: From eq. $y' = 2x + 2$
$\therefore$ L.H.S. of eq. $(ii), y' - 2x - 2 = (2x + 2) - 2x - 2$
$= 2x + 2 - 2x - 2 = 0 =$ R.H.S.
Hence, $y$ given by eq. $(i)$ is a solution of $y' - 2x - 2 = 0.$

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 Questions" 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

Verify that the function y = Ax (explicit or implicit) is a solution of differential equation $xy' = y\left( {x \ne 0} \right)$
→
Write the smallest reflexive relation on set $A=\{1,2,3,4\}$.
→
Kamal and Monica appeared for an interview for two vacancies. The probability of Kamal's selection is $\frac{1}{3}$ and that of Monika's selection is $\frac{1}{5}$. Find the probability that.
At least one of them will be selected.
→
If $\text{A}=\begin{bmatrix}1&2\\3&-1\end{bmatrix}$ and $\text{B}=\begin{bmatrix}1&0\\-1&0\end{bmatrix},$ find |AB|.
→
Prove that the determinant $\left|\begin{array}{ccc}x & \sin \theta & \cos \theta \\ -\sin \theta & -x & 1 \\ \cos \theta & 1 & x\end{array}\right|$ is independent of $\theta$.
→
Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{ax}^2+\text{bx}+\text{c}$
→
Write a unit vector in the direction of the sum of the vectors $\vec{\text{a}}=2\hat{\text{i}}+2\hat{\text{j}}-5\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\text{y}\hat{\text{j}}-7\hat{\text{k}}$.
→
Write the cartesian and vector equations of z-axis.
→
Find the values of $x, y,$ and $z$ from the following equation:
$\left[\begin{array}{c} {x+y+z} \\ {x+z} \\ {y+z} \end{array}\right]=\left[\begin{array}{l} {9} \\ {5} \\ {7} \end{array}\right]$
→
Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\overline{\text{B}})$
→