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Theory

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Procedure

Simulation

Posttest

References

Contributors

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Application to Ordinary Linear Differential Equations and Engineering Problems

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Beginner

Intermediate

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The value of differential operator

d^{2}y/dx^{2}

of the equation

x^{2}+e^{3x}-y^{2}=0

a:

2+9e^{3x}-2

Explanation

Explanation

b:

2x+3e^{3x}-2y

Explanation

Explanation

c:

2+3e^{3x}-2

Explanation

Explanation

d:

2x+3e^{3x}-2y=0

Explanation

Explanation

The complementary function of the differential equation

3y’’-12y=0

a:

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

Explanation

Explanation

b:

c_{1}e^{3x}+c_{2}e^{-2x}

Explanation

Explanation

c:

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

Explanation

Explanation

d:

c_{1}e^{2x}+c_{2}e^{-3x}

Explanation

Explanation

The complete integral of the differential equation

2y

’’

-3y=-

cos

x

a: cos

x

Explanation

Explanation

b: sin

x

Explanation

Explanation

c: -cos

x

Explanation

Explanation

d: -sin

x

Explanation

Explanation

Let

T(y)=r

be a linear map equation, where

T:F→F

is the operator defined as

T=D^{2}+PD+QI

and

P

,

Q

∈

R

. Then its solution is

a:

y_{0}+kerT

Explanation

Explanation

b:

y_{0}

Explanation

Explanation

c:

kerT

Explanation

Explanation

d:

y^{2}

Explanation

Explanation

The function

c_{1}e^{5x}+c_{2}e^{4x}+e^{x}

is the complete integral and then it satisfies which of the following differential equation

a:

y

’’

-9y

’

+20y=2e^{x}

Explanation

Explanation

b:

y

’’

-5y

’

+20y=0

Explanation

Explanation

c:

y

’’

-4y

’

+5y=e^{x}

Explanation

Explanation

d:

y

’’

-9y

’

+20y=12e^{x}

Explanation

Explanation

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