Given that y1, Y2 be a fundamental set of solution to the D. E. (e*y')' + y' + y = 0, x > 0 If the Wronskian W (y1, y2)(0) = 1 then W (y1, y2)(1) = %3D

Q: The values of C, and C₂ so that y(x) = C₁x + C₂ (-) satisfies the two conditions y(1) = 1 and y'(1)…

A: Given: yx=C1x+C2-13x2 To find the values of C1 and C2 such that y1=1 and y'1=-1.

Q: 3) y' dx-(xy+y*) dy-o Let the substitution v= i y vx; dy-vdx+xdv %3D )x*dy+(2xyy*) ax -o Let the…

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Q: d a value of r> 0 such that h(z) = z² +22³ + z + 1 has all its zeroes in D,(0).

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Q: What is the linear approximation of this function at (1,0) F(x, y) = (F(x, y) = (x² cos(x+y)) x²y 0…

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' +y = 0. If W(y1, Y2)(2) = e² , then W…

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Q: y(y2 + 1)dx + x(y2 – 1)dy = 0

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

Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

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Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: Let y1, Y2 be two independent solutions of (t 1)y"- ty' +y = 0. If W(y1, Y2)(2) = e2, then W(y1,…

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Q: Find a general solution to (ax+b)y"+ a(ax +b)y' – y=(ax+b)D, where a,b >0 with ax+b>0 for all x on a…

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Q: If y1 and y2 two solutions of (1 – a²)y" – 2xy' + n(n+1)y = 0; -1<x < 1 Show that W (y1, Y2) : 1-…

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Q: The graph of f(x)= x2 -1 is concave up on interval (-1,1)^O (0,1) 0 (-1,0) U (1, 0 )co…

A: Given,  The function fx = xx2-1  We have to find the interval in which the graph of  fx = xx2-1 is…

Q: If f (x, y) = V3 + y³ In (z +y°)e*in(zyty") +2² + 10y , then fz (1,0) = |3D %3D O 2 4. O 3

A: Given that fx,y=x3+y33lnx2+y2esinxy+y2+x2+10y3 First we have to find fxx,y where fx=∂f∂x

Q: Eliminate the Arbitrary Constant: y = c,x² + c2e¬* а. 2(х + 1)у' — (x? — 2)у" — х(х + 2)у %3D0 b.…

A: topic - differential equations

Q: Find the nonhomogeneous ODE whose general solution is y=c₁(x+1) ³+c₂(x+1)3³+x-1. (x + 1)² y" + (x +…

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

Q: a) Calculate [6x² (1-y) 0<x<1 0<y<1 0 otherwise b) Evaluate £xv (x, y) = {6x*(1-y) fxy…

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Q: If f (æ, y, 2) = x²y – 3yz + 2æz* , then f (2, 1, –1) is 2 O 5

A: If f(x,y,z) =x2y-3yz+2xz3, then f(2,1,-1) is

Q: Q.3\ Show the G.S (Y(x) = ce-3* + Cze*) is the solution of the ODE (y"+ 2 y'-3y -0)

A: Using complementary function

Q: The values of C₂ and C₂ so that y(x) = C₁x + ₂( satisfies 3x the two conditions y(1) = 1 and y'(1) =…

A: Given equation is y(x) = C1x + C2-13x2

Q: Find a GS of xy" - (2x + 1)y' + (x + 1)y = x²ex Hint: The homo portion of the DE may have a solution…

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Q: Eliminate the arbitrary constant for y = 4 + Cje3 Oy' + 3y + 12 = 0 Oy' - 3y + 12 = 0 %3D Oy" – 3y +…

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Q: find the general for al soluh'an 3yC3) (e)

A: The given differential equation, y(4)+3y(3)+3y(2)+y'=0

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.