Solve the following differential equation x dy dx +1=0;y(-1)=0 - Vidyadip

Question

Solve the following differential equation
$\text{x}\frac{\text{dy}}{\text{dx}}+1=0;\text{y}(-1)=0$

✓

Answer

$\text{x}\frac{\text{dy}}{\text{dx}}+1=0,\text{y}(-1)=0$
$\text{x}\frac{\text{dy}}{\text{dx}}=-1$
$\text{dy}=-\frac{\text{dx}}{\text{x}}$
$\int\text{dy}=\int-\frac{\text{dx}}{\text{x}}$
$\text{y}=-\log|\text{x}|+\text{C}$
Put x = -1 and y = 0
0 = 0 + c
c = 0
put c = 0 in equation (1),
$\text{y}=-\log|\text{x}|,\text{x}<0$

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 "4 Marks" from Differential Equations→Differential Equations — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{y}=1+\frac{\alpha}{\big(\frac{1}{\text{x}}-\alpha\big)}+\frac{\frac{\beta}{\text{x}}}{\big(\frac{1}{\text{x}}-\alpha\big)\big(\frac{1}{\text{x}}-\beta\big)}+\frac{\frac{\gamma}{\text{x}^2}}{\big(\frac{1}{\text{x}}-\alpha\big)\big(\frac{1}{\text{x}}-\beta\big)\big(\frac{1}{\text{x}}-\gamma\big)},$ find $\frac{\text{dy}}{\text{dx}}$

Find the inverse of the matrix (if it exists) given $\left[\begin{array}{ccc}2 & 1 & 3 \\ 4 & -1 & 0 \\ -7 & 2 & 1\end{array}\right]$

Prove that in any triangle ABC, $\cos\text{A}=\frac{\text{b}^2+\text{c}^2-\text{a}^2}{2\text{bc}},$ where a, b, c are the magnitudes of the sides opposite to the vertices A, B, C, respectively.

Form the differential equation of the family of circles having centre on y-axis and radius 3 units.

If xy = e^(x–y), then show that $\frac{\text{dy}}{\text{dx}} = \frac{\text{y (x - 1)}}{\text{x (y + 1)}}.$

Differentiate the following functions from first principles:
$\sin^{-1}(2\text{x}+3)$

A letter is known to have come either from LONDON or CLIFTON. On the envelope just two consecutive letters ON are visible. What is the probability that the letter has come from,
LONDON.

Discuss the continuity of the following functions:

$\text{f(x)}=\sin\text{x}+\cos\text{x}$
$\text{f(x)}=\sin\text{x}-\cos\text{x}$
$\text{f(x)}=\sin\text{x}\cos\text{x}$

Find the particular solution of the differential equation
2y e^x/y dx + (y – 2x e^x/y) dy = 0, given that x = 0 when y = 1.

The position vectors of points A, B and C are $\lambda\hat{\text{i}}+3\hat{\text{j}},12\hat{\text{i}}+\mu\hat{\text{j}}\text{ and }11\hat{\text{i}}-3\hat{\text{j}}$ respectively. If C divides the line segment joining A and B in the ratio 3:1, find the value of $\lambda\text{ and }\mu$