The general solution of d2ydx2-y-0 is

Given DE is nbsp; nbsp; d^2y/dx^2+y=0 Auxiliary equation is nbsp; nbsp;m^2+1=0 m=± i ∴ nbsp; nbsp; General solution is nbsp; nbsp; nbsp; ...

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Standard XII

Mathematics

General Solution of a Differential Equation

The general s...

Question

The general solution of $\frac{d^{2} y}{d x^{2}} + y = 0$ is

y = P c o s x + Q s i n x

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y = P c o s x

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y = P s i n x

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y = P s i n^{2} x

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Solution

The correct option is A $y = P c o s x + Q s i n x$
Given DE is
$\frac{d^{2} y}{d x^{2}} + y = 0$
Auxiliary equation is
$m^{2} + 1 = 0$
$m = \pm i$
$∴$ General solution is
$y = P c o s x + Q s i n x$

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Similar questions

Q. Show that

y = c_{1} e^{x} + c_{2} e^{- x}

is the general solution of the differential equation

\frac{d^{2} y}{d x^{2}} - y = 0

Which of the following differential equations has $y = c_{1} e^{x} + c_{2} e^{- x}$ as the general solution?
(a) $\frac{d^{2} y}{d x^{2}} + y = 0$
(b) $\frac{d^{2} y}{d x^{2}} - y = 0$
(c) $\frac{d^{2} y}{d x^{2}} + 1 = 0$
(d) $\frac{d^{2} y}{d x^{2}} - 1 = 0$

Q. The differential equation whose general solution is given by,

y = (c_{1} c o s (x + c_{2})) - (c_{3} e^{(- x + c_{4})}) + (c_{5} s i n x)

where

c_{1}, c_{2}, c_{3}, c_{4}, c_{5}

are arbitrary constants, is

Q. The general solution of the differential equation

\frac{d^{2} y}{d x^{2}} + 8 \frac{d y}{d x} + 16 y = 0

The differential equation whose solution is $y = c_{1} c o s a x + c_{2} s i n a x$ is
(Where $c_{1}, c_{2}$ are arbitrary constants)

[MP PET 1996]

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The general solution of d2ydx2+y=0 is

The correct option is A y=Pcosx+QsinxGiven DE is d2ydx2+y=0 Auxiliary equation is m2+1=0 m=±i ∴ General solution is y=Pcosx+Qsinx

The general solution of $\frac{d^{2} y}{d x^{2}} + y = 0$ is

The correct option is A $y = P c o s x + Q s i n x$
Given DE is
$\frac{d^{2} y}{d x^{2}} + y = 0$
Auxiliary equation is
$m^{2} + 1 = 0$
$m = \pm i$
$∴$ General solution is
$y = P c o s x + Q s i n x$