Solve- d y d x - 2 x 2 - x - find y when x - 0

dydx=2x^2+x y=∫ 2x^2+xdx y=2x^33+x^22 y=2(0)3+ 02 y=0 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Particular Solution of a Differential Equation

Solve: d y d...

Question

Solve:
$\frac{d y}{d x} = 2 x^{2} + x;$ find $y$ when $x = 0$

Open in App

Solution

$\frac{d y}{d x} = 2 x^{2} + x$
$y = \int 2 x^{2} + x d x$
$y = \frac{2 x^{3}}{3} + \frac{x^{2}}{2}$
$y = \frac{2 (0)}{3} + \frac{0}{2}$
$y = 0$

Suggest Corrections

Similar questions

Q. Solve:

\frac{d y}{d x} = x + 1;

find

y

when

x = 2

Q. Solve each of the following initial value problems:
(i)

y' + y = e^{x}, y (0) = \frac{1}{2}

(ii)

x \frac{d y}{d x} - y = \log x, y (1) = 0

(iii)

\frac{d y}{d x} + 2 y = e^{- 2 x} \sin x, y (0) = 0

(iv)

x \frac{d y}{d x} - y = (x + 1) e^{- x}, y (1) = 0

(v)

(1 + y^{2}) d x + (x - e^{- \tan^{- 1} y}) d x = 0, y (0) = 0

(vi)

\frac{d y}{d x} + y \tan x = 2 x + x^{2} \tan x, y (0) = 1

(vii)

x \frac{d y}{d x} + y = x \cos x + \sin x, y (\frac{π}{2}) = 1

(viii)

\frac{d y}{d x} + y \cot x = 4 x cosec x, y (\frac{π}{2}) = 0

(ix)

\frac{d y}{d x} + 2 y \tan x = \sin x; y = 0 when x = \frac{π}{3}

(x)

\frac{d y}{d x} - 3 y \cot x = \sin 2 x; y = 2 when x = \frac{π}{2}

(xi)

\frac{d y}{d x} + y \cot x = 2 \cos x, y (\frac{π}{2}) = 0

(xii)

d y = \cos x (2 - y \cos e c x) d x

(xiii)

\tan x (\frac{d y}{d x}) = 2 x \tan x + x^{2} - y; \tan x \neq 0

given that y = 0 when

x = \frac{π}{2}

Q. Solve each of the following initial value problems:
(i)

y' + y = e^{x}, y (0) = \frac{1}{2}

(ii)

x \frac{d y}{d x} - y = \log x, y (1) = 0

(iii)

\frac{d y}{d x} + 2 y = e^{- 2 x} \sin x, y (0) = 0

(iv)

x \frac{d y}{d x} - y = (x + 1) e^{- x}, y (1) = 0

(v)

(1 + y^{2}) d x + (x - e^{- \tan^{- 1} y}) d x = 0, y (0) = 0

(vi)

\frac{d y}{d x} + y \tan x = 2 x + x^{2} \tan x, y (0) = 1

(vii)

x \frac{d y}{d x} + y = x \cos x + \sin x, y (\frac{π}{2}) = 1

(viii)

\frac{d y}{d x} + y \cot x = 4 x cosec x, y (\frac{π}{2}) = 0

(ix)

\frac{d y}{d x} + 2 y \tan x = \sin x; y = 0 when x = \frac{π}{3}

(x)

\frac{d y}{d x} - 3 y \cot x = \sin 2 x; y = 2 when x = \frac{π}{2}

Q. Solve the differential equation

\frac{d y}{d x} = \frac{2 x (\log x + 1)}{\sin y + y \cos y}

, given that y = 0, when x = 1.

Q. Solve each of the following initial value problems:
(i)

y' + y = e^{x}, y (0) = \frac{1}{2}

(ii)

x \frac{d y}{d x} - y = \log x, y (1) = 0

(iii)

\frac{d y}{d x} + 2 y = e^{- 2 x} \sin x, y (0) = 0

(iv)

x \frac{d y}{d x} - y = (x + 1) e^{- x}, y (1) = 0

(v)

(1 + y^{2}) d x + (x - e^{- \tan^{- 1} y}) d x = 0, y (0) = 0

(vi)

\frac{d y}{d x} + y \tan x = 2 x + x^{2} \tan x, y (0) = 1

(vii)

x \frac{d y}{d x} + y = x \cos x + \sin x, y (\frac{π}{2}) = 1

(viii)

\frac{d y}{d x} + y \cot x = 4 x cosec x, y (\frac{π}{2}) = 0

(ix)

\frac{d y}{d x} + 2 y \tan x = \sin x; y = 0 when x = \frac{π}{3}

(x)

\frac{d y}{d x} - 3 y \cot x = \sin 2 x; y = 2 when x = \frac{π}{2}

(xi)
(xii)

Join BYJU'S Learning Program

Solve:dydx=2x2+x; find y when x=0

dydx=2x2+xy=∫2x2+xdxy=2x33+x22y=2(0)3+02y=0

Solve:
$\frac{d y}{d x} = 2 x^{2} + x;$ find $y$ when $x = 0$

$\frac{d y}{d x} = 2 x^{2} + x$
$y = \int 2 x^{2} + x d x$
$y = \frac{2 x^{3}}{3} + \frac{x^{2}}{2}$
$y = \frac{2 (0)}{3} + \frac{0}{2}$
$y = 0$