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pav-90 [236]
3 years ago
8

The equation3y′=3xy+2x2+2y2x2, (∗)can be written in the form y′=f(y/x), i.e., it is homogeneous, so we can use the substitution

u=y/x to obtain a separable equation with dependent variable u=u(x). Introducing this substitution and using the fact that y′=xu′+u we can write (∗) asy′=xu′+u=f(u)where f(u)=Separating variables we can write the equation in the formg(u)du=dxxwhere g(u)= . An implicit general solution with dependent variable u can be written in the formln(x)−=CTransforming u=y/x back into the variables x and y and using the initial condition y(1)=1 we findC=Finally solve for y to obtain the explicit solution of the initial value problemy=

Mathematics
1 answer:
Setler79 [48]3 years ago
5 0

Answer:

The explicit solution of the initial value problem is y = xtan(\frac{2}{3}lnx +\frac{\pi}{4}  )

Step-by-step explanation:

The step by step explanation is shown on the first uploaded image

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Amanda [17]
The answer is 21 because that’s when I finally touch a goldfish
8 0
3 years ago
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PLZ HELP I NEED BY 2:00 PM ATY LEAST!!! WILL GIVE BRAINLYIST<br> Find the value of in each case:
Pie

Answer:

23°

Step-by-step explanation:

Step 1:

< GEC + < ECG + < CGE = Δ ECG    Sum of a Δ

Step 2:

< IGF = < GCE    Corresponding ∠ 's

Step 3:

14° + 180° - 4x + 78° = 180°   Substitution

Step 4:

272° - 4x = 180°     Add / Algebra

Step 5:

- 4x = - 92   Subtract 272° on both sides

Step 6:

- 92 ÷ - 4   Divide

Answer:

x = 23°

Hope This Helps :)

7 0
3 years ago
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Let f(x)=2x-1 and g(x)=x^2 -3. Find (f o g)(-3)
anzhelika [568]
(f o g)(-3) = (f(g(-3))
Because g is on the inside, we carry out g first.

g(x) = x^2 - 3
Substitute -3 in for x.
g(-3) = (-3)^2 - 3 = 9 - 3 = 6
g(-3) = 6

Next, carry out f on the result of g(-3)
f(6) = 2(6) - 1
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So the answer is 11.

6 0
3 years ago
Which of the following statements are enough to prove that triangles EFI and GFH are similar?
SCORPION-xisa [38]

To Prove: ΔEFI ~ Δ GFH

Proof:

When two triangles are similar, their corresponding sides are Proportional and their corresponding interior angles are equal.

Two Triangles can be proven similar by following Similarity Criterion.

1. AA

2.SSS

3.SAS

→∠EFI=∠GFH-------[Vertically Opposite angles]

The Other statement which is needed to prove that triangles EFI and GFH are similar is

 Option C:→  ∠E ≅ ∠G

So, Two triangles ΔEFI and Δ GFH are Similar by Angle-Angle(AA) Criterion.

6 0
3 years ago
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The sum of three consecutive integers is 300. Find the Integers.
IrinaVladis [17]

Answer:

99+100+101

Step-by-step explanation:

3 0
3 years ago
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