Form the differential equation from the following primitives wher… - Vidyadip

Question

Form the differential equation from the following primitives where constants are arbitrart:$\text{y}=\text{ax}^2+\text{bx}+\text{c}$

✓

Answer

The equation of family of curves is
$\text{y}=\text{ax}^2+\text{bx}+\text{c}\ ...(1)$
where a, b and c is an arbitrary constant. so, we shall get a differential equation of third order.
Differentiating equation (1) with respect to x, we get
$\frac{\text{dy}}{\text{dx}}=2\text{ax}+\text{b}\ ...(2)$
Differentiating equation (2) with respect to x, we get
$\frac{\text{d}^2\text{y}}{\text{dx}}=2\text{a}\ ...(3)$
Differentiating equation (3) with respect to x, we get
$\frac{\text{d}^3\text{y}}{\text{dx}3}=0$
It is the required differential equation.

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

For what value of $\lambda$ is the function defined by
$\text{f(x)}= \begin{cases}\lambda(\text{x}^{2} - 2\text{x}), \text{if}\ \text{x} \leq0\\ \text{4x} + 1,\ \ \ \ \ \ \ \text{if}\ \text{x} > 0\end{cases}$

vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ are such that $|\vec{\text{a}}|=\sqrt{3},\big|\vec{\text{b}}\big|=\frac{2}{3}$ and $\big(\vec{\text{a}}\times\vec{\text{b}}\big)$ is a unit vector. write the angle between $\vec{\text{a}}$ and $\vec{\text{b}}.$

If I is the identity matrix and A is a square matrix such that $A^2 = A$, then what is the value of $(I + A)^2 = 3A$?

Write the projection of the vector $7\hat{\text{i}}+\hat{\text{j}}-4\hat{\text{k}}$ on the vector $2\hat{\text{i}}+6\hat{\text{j}}+3\hat{\text{k}}.$

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.
none of them will be selected.

Evaluate the following integrals:
$\int^\limits{2\pi}_{0}|\sin\text{x}|\text{dx}$

Find the maximum and minimum values of $f ( x )=\sin x$ in the interval $[\pi, 2 \pi]$.

If $\vec{\text{a}}=\hat{\text{i}}+2\hat{\text{j}}-3\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+4\hat{\text{j}}+9\hat{\text{k}}$, find a unit vector parallel to $\vec{\text{a}}+\vec{\text{b}}$.

A die marked 1, 2, 3 in red and 4, 5, 6 in green is tossed. Let A be the event the number is even, and B be the event the number is red. Are A and B independent?

An insurance company insured $2000$ scooter drivers, $4000$ car drivers and $6000$ truck drivers. The probability of an accidents are $0.01, 0.03$ and $0.15$ respectively. One of the insured persons meet with an accident. What is the probability that he is a scooter driver?