Download App

Differential Equation and Applications (p-1) — Maths (commerce) STD 12 Commerce / Arts — Question

Maharashtra BoardEnglish MediumSTD 12 Commerce / ArtsMaths (commerce)Differential Equation and Applications (p-1)2 Marks
Question
Find the differential equation by eliminating arbitrary constant from the relation $x^2+y^2=2 a x$.
✓

Answer

$
x^2+y^2=2 a x
$
Differentiating both sides w.r.t. $x$, we get
$
2 x +2 y \frac{d y}{d x}=2 a
$
Substituting value of $2 a$ in equation (1), we get
$
\begin{aligned}
& x ^2+ y ^2=\left[2 x +2 y \frac{d y}{d x}\right] x =2 x ^2+2 xy \frac{d y}{d x} \\
& \therefore 2 xy \frac{d y}{d x}= y ^2- x ^2 \text { is the required D.E. }
\end{aligned}
$

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.(2 Marks)" from Differential Equation and Applications (p-1)→Differential Equation and Applications (p-1) — all question types→Maths (commerce) STD 12 Commerce / Arts question papers→Maharashtra Board STD 12 Commerce / Arts question papers→Maharashtra Board question paper generator→

Similar questions

The company makes concrete bricks made up of cement and sand. The weight of a concrete brick has to be at least 5 kg. Cement costs ₹ 20 per kg. and sand costs ₹ 6 per kg. Strength considerations dictate that a concrete brick should contain a minimum of 4 kg of cement and not more than 2 kg of sand. Formulate the LPP for the cost to be minimum.
→
Calculate the cost of living index.
GroupBase YearBase YearCurrent Year
PriceQuantityPrice
Food13210170
Clothing15412160
Fuel & Lighting16420180
House Rent17518195
Miscellaneous1285120
→
Prepare the truth tables for the following statement patterns : (~p ∨ q) ∧ (~p ∨ ~q)
→
Find the adjoint of the following matrices : $\left[\begin{array}{cc}2 & -3 \\ 3 & 5\end{array}\right]$
→
Find $\frac{d y}{d x}$ if, :
$
x=2 a t^2, y=a t^4
$
→
Using the truth table, prove the following logical equivalences:
p ↔ q ≡ ~(p ∧ ~q) ∧ ~(q ∧ ~p)
→
A stock worth ₹ 7,00,000 was insured for ₹ 4,50,000. Fire burnt stock worth ₹ 3,00,000 completely and damaged there remaining stock to the extent of 75% of its value. What amount can be claimed undertaken policy?
→
Evalute : $\int \frac{d x}{5-16 x^2}$
→
Find the value Index Number using the Simple Aggregate Method.
COMMODITY BASE YEAR CURRENT YEAR
PRICEQUANTITYPRICEQUANTITY
A30224018
B40156012
C10381524
D50126016
E20282536
→
If p ↔ q and p → q both are true, then find truth values of the following with the help of activity

p ˅ q

$p \leftrightarrow q$ and $p \rightarrow q$ both are true if $p$ and $q$ has truth value $\square, \square$ or $\square, \square$.
$p \vee q$
i. If both $p$ and $q$ are true, then $p \vee q=\square \vee \square=\square$
ii. If both $p$ and $q$ are false, then $p \vee q=\square \vee \square=\square$
→