Download App

Differential Equations — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsDifferential Equations5 Marks
Question
verify that $\text{y}=\text{-x}-1$ is a solution of the differential equation $(\text{y}-\text{x})\text{dy}-(\text{y}^2-\text{x}^2)\text{dx}=0.$
✓

Answer

We have,
$\text{y}=-\text{x}-1\ ...(1)$
Differentiating both sides of (1) with respect to x, we get
$\frac{\text{dy}}{\text{dx}}=-1\ ...(2)$
Now,
$\frac{\text{dy}}{\text{dx}}-\frac{\text{y}^2-\text{x}^2}{\text{y}-\text{x}}$
$=\frac{\text{dy}}{\text{dx}}-(\text{y}+\text{x})$
$=--1-(-\text{x}-1+\text{x})$
$=-1+1=0$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\frac{\text{y}^2-\text{x}^2}{\text{y}-\text{x}}$
$\Rightarrow(\text{y}-\text{x})\text{dy}=(\text{y}^2-\text{x}^2 )\text{dx}$
$\Rightarrow(\text{y}-\text{x})\text{dy}-(\text{y}^2-\text{x}^2)\text{dx}=0$
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.(5 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

An automobile company uses three types of steel $S_1, S_2$ and $S_3$ for producing three types of cars $C_1, C_2$ and $C_3$. Steel requirements (in tons) for each type of cars are given below:
Steel
Cars
 
$C_1$
$C_2$
$C_3$
$S_1$
2
3
4
$S_2$
1
1
2
$S_3$
3
2
1
Using Cramer's rule, find the number of cars of each type which can be produced using $29, 13$ and $16$ tons of steel of three types respectively.
→
Solve the following differential equation:
$(\text{x}+\text{y})^2\frac{\text{dy}}{\text{dx}} = 1$
→
Evaluate the following intregals:
$\int\frac{\cos\text{x}}{(1-\sin\text{x})^3(2+\sin\text{x})}\ \text{dx}$
→
Solve the following equation
$\text{x}\cos^2\text{y dx}=\text{y}\cos^2\text{x dx}$
→
Compare the area under the curve $\text{y}=\cos^2\text{x}\text{ and }\text{y}=\sin^2\text{x}$ between $x = 0$ and $\text{x}=\pi.$
→
Using vector method, prove that the point is collinear:
A(6, -7, -1), B(2, -3, 1) and C(4, -5, 0)
→
Classify the following functions as injection, surjection or bijection: $f : R \rightarrow R,$ defined by $\text{f(x)}=\frac{\text{x}}{\text{x}^2+1}$
→
A card is drawn from a pack of 52 cards so that each card is equally likely to be selected. In which of the following cases are the events A and B independent?
A = the card drawn is a spade,
B = the card drawn in an ace.
→
A pair of dice is thrown. Let E be the event that the sum is greater than or equal to 10 and F be the event "5 appears on the first-die". Find $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)$. If F is the event "5 appears on at least one die", find $\text{P}\Big(\frac{\text{E}}{\text{F}}\Big)$.
→
Evaluate the following integrals:$\int_{0}^\limits{\frac{\pi}{2}}\frac{\sin\text{x}\cos\text{x}}{1+\sin^4\text{x}}\text{ dx}$
→