Solve the following equation xy dy=(y-1)(x+1)dx - Vidyadip

Question

Solve the following equation
$\text{xy dy}=(\text{y}-1)(\text{x}+1)\text{dx}$

✓

Answer

$\text{xy dy}=(\text{y}-1)(\text{x}+1)\text{dx}$
$\frac{\text{y}}{\text{y}-1}\text{dy}=\frac{\text{x}+1}{\text{x}}\ \text{dx}$
$\int\Big(1+\frac{1}{\text{y}-1}\Big)\text{dy}=\int\Big(1+\frac{1}{\text{x}}\Big)\text{dx}$
$\text{y}+\log|\text{y}-1|=\text{x}+\log|\text{x}|+\text{C}$
$\text{y}-\text{x}=\log|\text{x}|-\log|\text{y}-1|+\text{C}$

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 "3 Marks Question" 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 $y=3 \cos x-2 \sin x$, then prove that $\frac{d^2 y}{d x^2}-y=0$

Let A be the set of all human beings in a town at a particular time. Determine whether the following relations are reflexive, symmetric and transitive:
R = {(x, y): x and y live in the same locality}

For any two vectors $\vec{\text{a}}$ and $\vec{\text{b}}$ of magnitudes 3 and 4 respectively, write the value of $\big[\vec{\text{a}}\vec{\text{b}}\vec{\text{a}}\times\vec{\text{b}}\big]+\big(\vec{\text{a}}.\vec{\text{b}}\big)^2$

In the following, find the value of the constant k so that the given function is continuous at the indicated point:
$\text{f(x)}=\begin{cases}\text{k}\text{x}^2,&\text{x}\geq1\\4,&\text{x}<1\end{cases}\text{at x} =1$

There are $6\%$ defective items in a large bulk of items. Find the probability that a sample of $8$ items will include not more than one defective item.

Find the values of p so that the lines $\frac{{1 - x}}{3} = \frac{{7y - 14}}{{2p}} = \frac{{z - 3}}{2}$ and $\frac{{7 - 7x}}{{3p}} = \frac{{y - 5}}{1} = \frac{{6 - z}}{5}$ are at right angles.

Let $R_0$ denote the set of all non $-$ zero real numbers and let $A = R_0 \times R_0$. If $'*'$ is a binary operation on adefined by,
$(a, b) * (c, d) = (ac, bd)$ for all $(a, b), (c, d) \in A$
Show that '*' is both commutative and associative on $A$.

Each of the following defines a relation on $N: x, y$ is square of an integer $\text{x},\text{y}\in\text{N}$
Determine which of the above relations are reflexive, symmetric and transitive.

If $\text{A}=\begin{bmatrix}\cos\alpha&\sin\alpha\\-\sin\alpha&\cos\alpha\end{bmatrix},$ then verify that $A^TA = I_2.$

Define a symmetric matrix. Prove that for $\text{A}=\begin{bmatrix}2&4 \\5&6 \end{bmatrix}, A + A^T$ is a symmetric matrix where $A^T$ is the transpose of $A$.