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

Evaluate the following intregals:
$\int\frac{1}{13+3\cos\text{x}+4\sin\text{x}}\ \text{dx}$

By using the properties of definite integral evaluate:
$\int_0^{\frac{x}{4}} \log (1+\tan x) d x.$

In the set Z of all integers, which of the following relation R is not an equivalence relation?

xRy : if $\text{x}\leq\text{y}$
xRy : if x = y
xRy : if x - y is an even integer
xRy : if $\text{x}\equiv\text{y}\ (\text{mod 3})$

Evaluate the following intregals:
$\int\frac{2\text{x}+1}{(\text{x}+2)(\text{x}-3)^2}\text{ dx}$

If $\sin(\text{xy})+\frac{\text{y}}{\text{x}}=\text{x}^2-\text{y}^2,$ find $\frac{\text{dy}}{\text{dx}}$

Evaluate the following integrals:

$\int\sin^{-1}\sqrt{\text{x}}\text{dx}$

Find the points of local maxima or local minima and corresponding local maximum and local minimum values of the following functions. Also, find the points of inflection,

f'(x) = x⁴- 62x² + 9x + 15

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.

By using the properties of definite integrals, evaluate the integral $\int_{0}^{\frac{\pi}{2}} \frac{\sqrt{\sin x}}{\sqrt{\sin x}+\sqrt{\cos x}} d x$

Find the distance of the point P(3, 4, 4) from the point, where the line joining the points A(3, -4, -5) and B(2, -3, 1) intersects the plane 2x + y + z = 7.