(4) The general solution to (x +3)y" +5xy' - y = 0 converges at least on and is y = Co x2+ r6 +... x+ x5+ x7 + ...

Q: 2) f(x) = xx| - T <x<T Ans. Odd

A: the given function is  f(x)=xx

Q: 13. If f(x) = 1 / (5 + 7x) , find S f(x) by using a u-substitution. Show the u-substitutions.

A: Given, fx = 15 +7x  We have to find ∫fx using u substitution

Q: Calculate s'(n) (8n + 5 s(n) = 2n-6/ 6

A: The given function is s(n)=8n+52n-66 To find the s'(n). Derivative formula:…

Q: √√3+ rdr then 0 (2)=√√3+230 I X

A:

Q: Suppose that a particular function f satisfies f" (x) = 12x? + 6x + 8, ƒ(0) = 1, f' (0) = –1. Then…

A:

Q: f (x) = 2x+7 if -5=Xcl 8 If X = 1 14X=3 if 11x-2 31 If x > 3 IS this continuous at X=1 ? formula…

A: Any function f(x) is continuous at x=a if  lim x -&gt; a f(x) = f(a) i.e. Functional value at that…

Q: Find the approximate integral of the following function using Simpson's 3/8 rule and determine the…

A: Since you have asked multiple questions, we will solve the first one for you. If you want any…

Q: 13. Find ƒ. (1)ƒ'(x)=x² + 3√x (2) f(t)=2cost+sec²t,-/2 <t</2,ƒ(π/3)=4; (3)ƒ*(x) = 6x+sinx.

A:

Q: Find the 2nd solution using reduction of order. t²y" - 4ty +6y=0;t> 0; y₁=t²

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Q: (1+ 2.x² þ" – 4.xy' + 4y=0 yı(x) = x

A:

Q: ) If f(x) = (0 <* < 1) (-1 < * < 0) expand f(x) in the form c,P(x).

A: According to our company policy i am supposed to answer ony one question at a time.  For the rest…

Q: Show by direct substitution that (-1)"+1 y = n-1 is a particular solution to (x + 1)y" +y' = 0

A:

Q: 13. Show that (a) (b) f x²s+¹e-ax² dx = x²se-ax² dx = s! 2as+1; (s — 1/1 ) ! 2a³+1/2

A: 13. (a) I=∫0∞x2s+1e-ax2dx Let us assume x=za⇒dx=12a·z-12dz. Hence the limits will change…

Q: 5. (i) Show that +C, 1+u (a) du = 2 In u(1+ u) 1 dx du , using the substitution u = x. (b) J x(1+…

A: Given,

Q: 8. Find f'(x) for (a) f(x)=(x² +3x+1)(2x+3) 2x-3x+1 (b) ƒ(x)= %3D

A: We need to find the derivative of the given functions. For (a),

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = Ax x + x+ +В х + x+ x²+ x³ + and converges on…

A:

Q: 3. (3y² + xcos xy) sh a) d) al + (3x2 + ycos xy) = 0 dx y + sen xy + x³ = 0 y2 + sen xy + x³ = 0 y²…

A: The given equation is;  (3y2+xcosxy) dy/dx +(3x2+ycosxy) =0

Q: If f(x) = > anx", where the coefficients in the ex- n=0 pansion satisfy En(n + 2)anx" + (n –…

A:

Q: x+3-2 f(x) = f'(1)? x+2

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Q: f"(x) = 20x3 + 12x2 + 4 with the initial conditions f(0) particular f(x). = 8 and f(1) = 5. Det

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Q: 8. Find f(4) if f(0) >0 and [f(x)]² = [(f(t))² + (f'(t))²]dt + 4.

A: We do this using Lebniz rule for differentiation under integral sign. The detailed solution is…

Q: Show that y" + ay' = b, wherein a and b are constants, can be reduced to y' =+ C₁e-ax using 2…

A:

Q: (a) Find the approximate integral of the following function using Simpson's 1/3 rule and (b)…

A: Note: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question…

Q: Compute r"(t) and r'''(t) for the following function. r(t) = (7t2 + 4,t + 3,6)

A:

Q: If f(x) = 3x² +5+ (4x – 3)* | , then f '(x) is - + 5+ (4x – 3)*]" [4(4x – 3)'] B. [3* +5+ (4r -…

A: Given:            fx=3x2+5+4x-349 Solve: f'x           ddxfx=ddx3x2+5+4x-349

Q: 21. Find particular solution of the differential oquation-2(x+ 1) Y.given x 0,

A: Givne that  The differential equation  To find the particular solution of the differential equation

Q: 2) f(1)=47² -ť², (0<t<2x)

A:

Q: 1) If h(a) = a + 1, find h-(x). (A) h-(x) = 3+ (x+ 2)3 (B) h-(x) = V – I (C) h-(x) = 2a3 – 3 %3D %3D…

A:

Q: Let X ~ T(a, B). If E(X) = aß and E(X²) = aß² + a² ß². If â = X, find the method of B moments…

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Q: 18) Suppose P'(x) = 5ex - 6x³+ 4x and P(0) = -9. Find P(x).

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Q: 9. Given that 00 2n+3 f x) - Σ(-1)" (2n +1)! n=0 Find f '(0)

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Q: Q2/ prove that L{f"} = s²F(s) – sf(0) – f (0)

A:

Q: Let f(x) = x' - 5æ + 7x- 4x 3. Then f'(x) is f'(1) is f"(x) is and f''(1) is

A: Given: f(x) = x7-5x5+7x3-4x-3

Q: 3. Solve xy" + y = 0 given that y(1) = 1, y(2) = 2 taking h = 0.25 using finite difference method.

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Q: Express f(x) = x2 / x2+4 into partial fractions and hence show that ∫02f(x) dx = 2 - π/2.

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Q: 5) f(x) =x' - T <x<TI Ans. Odd

A:

Q: If f(x) = then f"(x) = = X √ ² ( 2³ + (t³ + 4t² + 5) dt 0 ←

A: Let,Using integration formula So,If  dtPut , dt = F(t)Then So,

Q: If y = (1 + x)(1 + x²)(1+x*)....(1 + x* ) then at x = 0 is - dx

A: Introduction :

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.