Q1 (A): Find the deflection equation of simply supported beam which shown in figure by using the Fourier half range sine expansion. (EI=constant). (B): Find the general solution of O.D.E y" - y = sinh(x) + cosh(x) 2.0 kN/m 计 2m2m 2m

Q: „M\ 3 Evaluate: [Answer: 4/2 (1 – j] 245°

A: The general form of a complex number is given by z=x+jy, where x, y are two real numbers and j=-1.…

Q: S (b) /: 8. (а) sin (x - т) dx; и 3 х — т 5x* .5 dx; и — х° + 1 (x5 + 1)2

A: (a) Consider

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

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A: Given:The motion is described by 3y''+4y=0, y0=5, y'0=6. We have to find the amplitude of the…

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Q: 6) —— (y² + z²)u₂ +xzu₂ − xyu¸ = 0

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Q: (77) (04-70° + 180² - 200+ 200+8) V = 0

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Q: (1) хdy — ydx — Vx? + у? dx (2) — Зу? — у? sin x dx (3) (x2 + 1)4 — у2 + 1 dy dx

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Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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Q: Find a particular solution Yp = A cos wt and enter the amplitude factor A rounded to 4 decimal…

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Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: a) Use the Euler formula, e¹⁰ (cos(0) + i sin(0))" = cos(n) + i sin(n). b) Suppose y(t) = e-2t eit…

A: In this question, we will find the solution to the given problem.

Q: A string with motionless ends at z = 0 and z = 1 vibrates according to the wave equation Fu Fu ət²…

A: Given: A string with motionless ends at x=0 and x=1 vibrates according to the wave equation…

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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Q: Q.No.3: a) Solve Cauchy-Euler equation d'y 3x3 dx3 d'y + 9x2 + 6x dx2 dy 6y = 1+ x3 dx -

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Q: Integrate the following using substitution 1) z5 (9z6 – 7)8 dz 2) S dy 4 y3 2-5y4

A: Given that: 1. ∫z5(9z6-7)8dz   NOTE: As per our answering guidelines, we can only answer 1 question…

Q: Use approbriate ferm of chain rule to fird %3D

A: Given  z=cos(x)sin(y)x=u−vy=u2+v2

Q: 4) Find the following by using the substitution z = tan D S 5 dt sint - cost cos e de ii) sin cos 0…

A: Note : As per our Guidelines , we can solve first one as your all parts are not too small . Please…

Q: Find a particular solution Yp A cos wt and enter the amplitude factor A rounded to 4 decimal places.

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Q: x = t – 1 * (D) : y = 2t + 3 x = - t'+ 1 (D') : y = t' - 2

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

Q: Solve using variation of parameters: y" - 2y' + y = e(1+1²) + 3et p= ₁ ¹ + ₂ tet (Use 2 decimal…

A: Using Variation of Parameters Method we have to find the u1(2).

Q: A particle moves on an axis “x" with variable speed v(t) starting from t= 0. Calculate for each…

A: According to question, Particle moves on x-axis direction, We have, Variable speed, v t = 10 + 4…

Q: 8. (y – In æ) dæ + (x +1) dy = 0, y(1) = 10 Ghenoral Form : y' + Pixly= Q(x) I (x): PLk) du : Final…

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Q: Consider the Riccatti equation  v'= v^2-7v/x +8/x^2 a) Use the substitution  v= y'/y  obtain the…

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Q: A mass that weighs 8 pounds stretches a spring 6 inches. The system is acted on by an external force…

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Q: 6. (6x°-4x² +1)*

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Q: - (D' - 4)y = x'e"

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Q: 7) Determine an eq ,in (x) and (y) , and then find a) y sec 1t , x csc-1t b) y = (sin 0)* ,x = (cos…

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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: PART A Let x(t) = 5 cos(t) and y(t) = 3 sin(t) At t = 6, x(6)= = y(6) = speed (6) PART B Now, if we…

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

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

Q: Ben can wash a car in 2 hours while his younger brother James can do it in 3 hours. How long will it…

A: In 1 hour Ben can wash 12 part of car. in 1 hour his younger brother can wash 13 part of car.