3. Solve the initial value problem. Determine the interval in which the unique solution of the initial value problem exists a²y + xy = x² In c, y(1) = 2

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A: The given differential equation is  y'=9x2sqrt(y2-1)/y

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A: fx=2x+3,x&lt;15,x≥1

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A: Given, -3secθ=2 Divide by -3 on both sides, -3secθ-3=2-3 we have  secθ=-23

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A: Since you have asked multiple question, we will solve the first question for you as per our guide…

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A: Note:- According to our guideline i didn't solved multiple questions .so please again repost the…

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Q: Which of the following is true? O Scos(3x)cos(4x)dx= [ r cos(x) + cos(7x) dx B Jsin(3x)cos(4x)dx= […

A: Option D

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A:

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A: The objective is to find the exact value of cscA.

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A: To find out the integration.

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A: Here , we have given a indefinite integral in which two functions are given now we will solve this…

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Q: The definite integral (10+-2-3-ar+5)dx is equivalent to A 2 (at- 3r+ 5)de B 2(10-2-6r) ds…

A: LetI=∫-5510x5+x4-2x3-3x2-6x+5dxWe know that ∫-aax2n+1dx=0Apply the Sum Rule:…

Q: In tan"u du where n is any integer, we use the transformation for tan²u= sin²u cos?u

A: ∫(tan2u)du then put x=tan(u) then u=tan-1(x) and du=dxx2+1

Q: The marginal cost for a company to produce q items is given by MC(q)=0.004q^2−0.8q+635. The​…

A: Given that the marginal cost for a company to produce q items is given by       MC(q) = 0.004q2 -…

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Q: Find 2f (x) dx jf f (x) dr=2 and f (x) dr= - 6

A: We have to find out

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A: To find the antiderivative.

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Q: 2r+3, x<1 f (x) dx if f (x) = 5, Evaluate x21 A 21 B 19 28 D 16

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A: Given ∫sin4xcos5xdxWe can simplify this and write as∫sin4x(cos2x)2cosxdx

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A: Let us take  A = (−1,2,4), B = (0,4,8), and C(1,1,5).

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A: We need to solve the integral.

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A: Please see the below picture for detailed solution.

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A: To simplify the above integral we have to use trigonometric technique .

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Q: Evaluate: fevdx. @ -2ev(/x+1)+ Cc A ® =2ev(/x-1)+ c 2ev(/x +1) + C 2ev(x-1) D +C 2

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Q: Use the Laplace transform to solve the given integral equation f(t) + (t – r)f(t)dt = t f(t) =

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A: Let's find.

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A:

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A: Option C

Q: Question 9 x² – 4 Evaluate: V A =Vx² - 4 – 2 sec-+ c =V x2 – 4 + sec¯ + C = 2/x? – 4 + sec + C D x2…

A: The integration of the integral is sqrt(x2-4)/x.