Are y₁ (1) = x, y₂(x) = ze² a fundamental set of solution for the equation r²y" − x(x + 2)y' + (x + 2)y=0, 0 < x? Justify your answer.

Q: #16. Simplify xy-1 4 ху 1/32 3

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Q: x²y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 3. Determine if the two solutions in Questions 1 and 2 are…

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Q: Obtain the particular solution for the equation 2(x³ + 7)y' = x?y when x = 1, y = 4.

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Q: Y4(t) = ¿et is a particular solution of y" – y = 2e3t. The general solution of /" – y = 2e3t is…

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Q: ,(x) = (x-x+1) y'(x)+3y'(x)+9 y(x) = 5x' +1 true false

A: False

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Q: 2x y" +5xy' + y = 3x +2 Answer y(x) = +은+2+

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Q: (C) y" + 21y+8x=y" + 5y' + e²*

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Q: Are the functions y₁(x) = e, y2(x) = ze a fundamental set of solutions for the equation y" - 2y + y…

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Q: Determine (without solving the problem) an interval in which the solution of (9-1²)y + 2ty = 4t²,…

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

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Q: "+2y(y)² = 0 =1^²)={1^²/ LV=X+C₂ y(x) = c₂e¹1* - 1 . (C₂-y)² + x² = C₁ :C. -In(c 2) 71

A: Given differential equation

Q: Solve the DE: (2-x) y³ +(2x-3) y'' - xy' + y = 0, x<2, given that y(x) = ex is a solution of the…

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Q: 1) Find the general solution of the equation x³y"" - 2x2y" - 4xy' + 8y = x² + lnx.

A: In this question we will find the general solution of the differential equations.

Q: 2a) find a solution of y" (x) = y(x) that passes the origin and go trhout the point (In(2),-).

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Q: Q4. (a) Show that the substitution r= e' reduces the equation ar'y" + bry' + cy = g(x) to an…

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Q: 1) Find the general solution of the equation x³y" - 2x²y" - 4xy' + 8y = x² + Inx.

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Q: Solve the equation 2 x " y " + 3 x y = (1 + x ) y = ху - which has a regular singula Point x = 0.…

A: Here both p(x)=32xand q(x)=−1+x2x2 aree non analytic at x=0 so 0 is a singular point. But both…

Q: Consider the following equation: x?y" + 2xy' – 2y = 0; x > 0; y = y(x) (1) 1. Verify that y, (x) = x…

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Q: Write the equation „dr te +x dt dr in the form of +p(t)x=q(t). Then identify p(t) and q(t). dt…

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Q: Let a +0 be any real number different from 0. If y = f(x) is the solution of y" – ay" = -48+48ax,…

A: the given differential equation is  y'''- a y''= -48 + 48 a x      .....(1) the associated…

Q: What is the particular solution if y(1)=0? 1/2 xy = y + (x² + y³)"

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Q: b) Solve ди Ət ди +3x = 1+u, Әх -8AHAB, u(x,0) = f(x). t > 0,

A: Given pde is  ∂u∂t+3x∂u∂x=1+u,  -∞&lt;x&lt;∞, t&gt;0 and u(x,0)=f(x) we have to solve this pde

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A: Given differential equation is                  dydx(1+2y)-2x=0      ⟹   (1+2y)dy=2xdx Intergrating…

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Q: Solve the following: 1. y'=√x+y+I 2. 2xy + y³e-2 = 2xy. (Bernoulli) 3. (x-y)y' = x+y, y(1) = 1. 4.…

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Q: Solve the given differnetial equation by undetermiend coefficents  y'' + 2y' = 2x +7 -e-2x   y(x)…

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A: Given :