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

Question

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

✓

Answer

The equation of family of curves is $\text{y}=\text{cx}+2\text{c}^2+\text{c}\ ...(1)$ where c is an arbitrary constant. This equation contains only one arbitrary constant, so we shall get a differential equation of first order. Differentiating equation (1) with respect to x, we get $\frac{\text{dy}}{\text{dx}}=\text{c}\ ...(2)$ $\Rightarrow\frac{\text{y}}{2}\frac{\text{dy}}{\text{dx}}=\text{a}\ ...(2)$ Putting the value of a in equation (1), we get $\text{y}=\text{x}\frac{\text{dy}}{\text{dx}}+2\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\Big(\frac{\text{dy}}{\text{dx}}\Big)^3$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→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

If $A=\left[\begin{array}{ll}2 & 5 \\ 3 & 8\end{array}\right]$ then find $A ^{-1}$.

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.
Both of them will be selected.

Show that the Signum Function $f : R \rightarrow R$, given by $f(x)=\left\{\begin{array}{l}1, \text { if } x>0 \\ 0, \text { if } x=0 \\ 1, \text { if } x<0\end{array}\right.$ is neither one$-$one nor onto.

If in a binomial distribution mean is 5 and variance is 4, write the number of trials.

Find the general solution of the differential equation $\frac{d y}{d x}=\sqrt{4-y^{2}}(-2<y<2)$

If $\text{y}=\sin^{-1}(\sin\text{x}),-\frac{\pi}{2}\leq\text{x}\leq\frac{\pi}{2}.$ Then, wrrite tha value of $\frac{\text{dy}}{\text{dx}}\text{ for x}\in\Big(-\frac{\pi}{2},\frac{\pi}{2}\Big).$

Given two independent events A and B such that P(A) = 0.3 and P(B) = 0.6. Find
$\text{P}(\text{A}\cap\text{B})$

Verify that the function $y = x \sin x ($explicit or implicit$)$ is a solution of differential equation $xy' = y + x\sqrt {{x^2} - {y^2}} $ $\left( {x \ne 0\,\,and\,\,x > y\,or\,x < - y\,} \right)$

For what vaiue of $\lambda$ are the vectors $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ perpendicular to each other?

Write the value of $\big[\hat{\text{i}}+\hat{\text{j}}\hat{\text{j}}+\hat{\text{k}}\hat{\text{k}}+\hat{\text{i}}\big].$