All categories

4 years ago

Show that y=2e^(−x) cos(x)−e^(−x) sin(x) is a solution to y''+2y'+2y=0.

Mathematics

1 answer:

Furkat [3]4 years ago

7 0

Answer:

y=2e^(−x)cosx−e^(−x)sinx

Satisfies the equation

Step-by-step explanation:

Answer:

y=2e^(−x)cosx−e^(−x)sinx

y = e^(-x)[2cosx - sinx]

Find y' and y" using product law

y' = -e^(-x)[2cosx - sinx] + e^(-x)[-2sinx - cosx]

y' = -e^(-x)[2cosx - sinx + 2sinx + cosx]

y' = -e^(-x)[3cosx + sinx]

y" = e^(-x)[3cosx + sinx] - e^(-x)[-3sinx + cosx]

y" = e^(-x)[3cosx - cosx + sinx + 3sinx]

y" = e^(-x)[2cosx + 4sinx]

y" + 2y' + 2y

e^(-x)[2cosx + 4sinx] - 2e^(-x)[3cosx + sinx] +2e^(-x)[2cosx - sinx]

e^(-x)[4sinx - 2sinx - 2sinx + 2cosx - 6 cosx + 4cosx]

= e^(-x) × 0

= 0

You might be interested in

On Friday night, Leah ate a pizza for dinner and had 1/3 of the pizza left over. On Saturday,

Vsevolod [243]

Answer:

7/30.. hope this helps..

8 0

3 years ago

Find each missing angle of the trapezoid

zimovet [89]

Answer:

∠J = 107°

∠K =107°

∠L = 73°

∠M = 73°

Step-by-step explanation:

Angle J + angle M = 180°

(10x - 33) + (4x+17) = 180

simplify:

14x -16 = 180

14x = 196

x = 14

∠J = 10(14) - 33 = 107°

∠M = 4(14) + 17 = 73°

7 0

3 years ago

A guy stole $100 from a stores cash register, let's call it Dave's. He bought $70 in groceries, and paid with the $100 bill. The

sergij07 [2.7K]

Well by calculations i would say 100

8 0

3 years ago

Read 2 more answers

Kedir bout 200 eggs for Birr 50 Birr and sells them for Birr 0.30 each.

ella [17]

Answer:

Yes, Kedir made profit.

Step-by-step explanation:

0.30 x 200 = 60 Birr

60 Birr is more than 50 Birr

He made profit of 10Birr, which is 20% of 50 Birr

8 0

3 years ago

Which expression is equivalent to the one in the picture?

Ne4ueva [31]

Answer:

Step-by-step explanation:

To convert a root to a fraction in the exponent, remember this rule:

$\sqrt[n]{a^{m}}=a^{\frac{m}{n}}$

The index becomes the denominator in the fraction. (The index is the little number in front of the root, "n".) The original exponent remains in the numerator.

In this question, the index is 4.

The index is applied to every base in the equation under the root. The bases are 16, 'x' and 'y'.

$\sqrt[4]{16x^{15}y^{17}} = (\sqrt[4]{16})(\sqrt[4]{x^{15}})(\sqrt[4]{y^{17}}) = (2)(x^{\frac{15}{4}}})(y^{\frac{17}{4}}) = 2x^{\frac{15}{4}}}y^{\frac{17}{4}}$

To find the quad root of 16, input this into your calculator. Since 2⁴ = 16, $\sqrt[4]{16}$ = 2.

For the "x" and "y" bases, use the rule for converting roots to exponent fractions. The index, 4, becomes the denominator in each fraction.

$2x^{\frac{15}{4}}y^{\frac{17}{4}}$

5 0

4 years ago