Download App

Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations3 Marks
Question
verify that $\text{y}=\text{cx}+2\text{c}^2$ is a solution of the differential equation $2\Big(\frac{\text{d}\text{y}}{\text{dx}}\Big)^2-\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=0$
✓

Answer

We have,
$\text{y}=\text{cx}+2\text{c}^2\ ...(1)$
Differentiating both sides of (1) with respect to x, we get
$\frac{\text{dy}}{\text{dx}}=\text{c}\ ...(2)$
Now,
$2\Big(\frac{\text{dy}}{\text{dx}}\Big)^2+\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}$
$=2\text{c}^2+\text{cx}-\text{cx}-2\text{c}^2=0$
$\Rightarrow\Big(\frac{\text{d}\text{y}}{\text{dx}}\Big)^2+\text{x}\frac{\text{dy}}{\text{dx}}-\text{y}=0$
Hence, the given is the solution to the given 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 "Solve the Following Question.(3 Marks)" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Show that $\text{y}=\text{Ae}^{\text{bx}}$ is a solution of the differential equation $\frac{\text{d}^2\text{y}}{\text{dx}^2}=\frac{1}{\text{y}}\Big(\frac{\text{dy}}{\text{dx}}\Big)^2.$
→
If $\bar{c}=3 \bar{a}-2 \bar{b}$ prove that $[\bar{a} \bar{b} \bar{c}]=0$
→
Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.
→
Find fog and gof if:$f(x) = e^x, g(x) = log_ex$
→
The mean of a binomial distribution is 20 and the standard deviation 4. Calculate the parameters of the binomial distribution.
→
Evaluate the following:

$\int x^2 \sin 3 x d x$

→
Find the inverse of each of the following matrices (if they exist) : $\left[\begin{array}{lll}1 & 3 & -2 \\ -3 & 0 & -5 \\ 2 & 5 & 0\end{array}\right]$
→
Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{|x|}\cos\Big(\frac{1}{\text{x}}\Big), & \text{ x}\neq 0\\0 &\text{ x} = 0\end{cases}\text{at x}=0$
→
In ∆ABC prove the following : $\frac{b-c}{a}=\frac{\tan \frac{B}{2}-\tan \frac{C}{2}}{\tan \frac{B}{2}+\tan \frac{C}{2}}$
→
Solve: $\cos\big(\sin^{-1}\text{x}\big)=\frac{1}{6}$
→