Solve- d y d x - x-1 - find y when x - 2

dydx=x+1 y=∫ x+1dx y=x^22+x x=2 y=(2)^22+2 y=4 ...

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Standard XII

Mathematics

General Solution of a Differential Equation

Solve: d y ...

Question

Solve:
$\frac{d y}{d x} = x + 1;$ find $y$ when $x = 2$

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Solution

$\frac{d y}{d x} = x + 1$
$y = \int x + 1 d x$
$y = \frac{x^{2}}{2} + x$
$x = 2$
$y = \frac{(2)^{2}}{2} + 2$
$y = 4$

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

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

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Solve: dydx=x+1; find y when x=2

dydx=x+1y=∫x+1dxy=x22+xx=2y=(2)22+2y=4

Solve:
$\frac{d y}{d x} = x + 1;$ find $y$ when $x = 2$

$\frac{d y}{d x} = x + 1$
$y = \int x + 1 d x$
$y = \frac{x^{2}}{2} + x$
$x = 2$
$y = \frac{(2)^{2}}{2} + 2$
$y = 4$