7/24/2019 MATE CASO 2

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Comprobemos:

yn=C1 ex+C2x e

x

yp=

1 (x ) ex+

2 (x )x ex

exxe

x

W e

2x+xe2xe2xx=e2x

exex+xex

1 xex

W1 2x e

2x

2exex+xex

ex0

W2 2e

2x

ex2e

x

1=2 xe2x

e2xdx

1=2

x2

2

1=x2

7/24/2019 MATE CASO 2

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2=2 e

2x

e2xdx

2=2x

x2 ex+2x2 ex

x2ex

1 ex+2e

4x

exe4x

W 4 e3x

+e3x

=5e3x

ex 4e4x

1 e4x

W1 30e

5x

30ex4e

4x

ex0

W2

30

ex30ex

7/24/2019 MATE CASO 2

3/3

1=

30e

5x

5e3x

dx

2=

30

5e3x

dx

1=6 e2xdx 2= 6 e

3xdx

2x=

3x=

2dx=d

3dx=d

dx=d

2 dx=

d

3

1=6

2 ed 2=

6

3 ed

1=3e2x

2=2e

3x

yp=3x+(2ex)

yp=5ex