[1 0 Го then find the solutions of the given Q2. a) SupposeA='0 o 'and b(f) 1 | 19 7 31 sint] - dX dX system of equations (i) and (ii) = AX + b(t). AX wwww wwwww dt dt

Q: Consider the Riccatti equation Please answer all parts. v'=v2-(7/x)v+8/x2 a) use the substitution…

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Q: 1) S dx 9-x2 dx 2) J2y-2 x2Vx2 -2 3) dx 2 V1-x2 |3D

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Q: 2. Find F'(x) if F(x) =tan(3x² + 2x). Solution: U= du dx 11 dy du dy dx 11

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Q: If r(t) = = cos(-3t)i + sin(−3t)j – 10tk compute r' (t)= i+ i+ (cos (-3t))/3 and fr(t) dt= (-sin…

A: r(t)=cos(-3t) i+sin(-3t) k-10tk

Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d²y dx2 dy + 9x? + 6х— — бу %3 1+x3 dx

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A: A differential equation of the form Mdx+Ndy=0 is said to be exact differential equation if it…

Q: (D3 - 5D² + 8D-4)y=e2x, Find Y = Yc - Yp a. 2x cé + Cẻ +C xe O C. -2x O b. 2x 2x °°€₁p² + €₂²³ +…

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Q: 1 1 (ах + 1) dy + + x² y? y3 = 0 dx

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Q: Solve the Cauchy euler equation 3x2+ 6x-6y = 3 + Inx d²y + 6x2-6y = 3 + lnx³ dx3

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Q: The particular solution for the equation: (d2y/du2) + (dy/du) + y = e3u yp(u) = ? a) (1/11)e3u…

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Q: Q12) Solve the eq с ес 1-j (1) e" 1+j

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

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Q: Use D-operator methods to solve (1) (0²+16)y= tsint Cii) (D²+D+5)y =t coszt %3D

A: Given : i) (D2+16)y=tsint ii) (D2+D+5)y=tcos2t.

Q: 5) x2. dx = x² + 3xy + y², (c) dr = 2 = 3v, + 3x' (d) (1 - y)' + By - 5x = 0.

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Q: d²y Find and dx then simplify whenever possible. dx2 1) y = 3t5 – 2t x = 4t3 2) y = t-3 – 7 x = t2 –…

A: We have to find first and second derivative for the given parametric function.

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A: The given differential equation is y''+2y'+y=2e-x1-xsin 3xy''+2y'+y=2e-x-2xe-xsin 3xHere the…

Q: 1 y" + 3y' - 18y = 0 2 y"-14y' +49y = 0 y" + 2y' +10y = 0 y"" — 7y — бу = 0 3

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Q: 1) S“(cosx)" dx. 2) Г(-4). 3) В (10,9) 4) Sº x° e-2* dx Ja-x)i 5) o

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Q: Select all equations that are equivalent to a-6z 16. a + 6x 9 0 O b a + 6x +9 = 16 Oc a+6x + 9 = 25…

A: Solution:-Given equation,     x2+6x=16  —1let us see and solve each option given,a…

Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: ) (2ху — tanу)dx + (x* — хsec*y)dy 3D 0

A: Given: (2xy-tany)dx+(x2-xsec2y)dy=0

Q: What is the general solution of 3 (3x² + y°) dx - 2rydy = 0 ? O== c (9z2 + y?) = c (9z? - y°) = c…

A: Topic = Differential equation

Q: Q4) Use separation of variables method to solve: d²u ди ax² + =u where u(0, y) = 0 and ду du(x,0) by…

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Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: 9) Solve the equations by Cramer's rule: 2x-y + 3z=-3 3x+3y-z=() -x-y+z=-4

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Q: 1) (10) The equation given below; a) prove that it is complete b) solve [(2xy + 1)dx + (x² + 4y)dy…

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Q: Q.1) A- If x=u- vandy = u + v then show the equations that correspond to Əw dw Əw. aw. the following…

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Q: 2) Solve the following first-order linear equations (assuming that y is the dependent variable and…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.