41. Let a, b, r be constants. Show that y = Ce-kt +a + bk k sin rt -r cos rt k2 +r2 is a general solution of dy dt -k(y - a - b sin rt)

Q: Find the total differential. w = x7yz9 + sin(yz) dw = 7x°yz° dx + 6.9 7_9 +2 cos (yz) )dy + (9x'yz°…

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Q: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

Q: If f(x, y) = 2x² – 8y², then the total differential of f at x = 1 and y = -2 is : - O df = 32 dx + 4…

A: In total differential take the derivative of each terms, put the given values and simplify.

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A: The third order equation is d3ydt3-2y=0. Consider dydt=p, d2ydt2=q⇒p'=q, q'=2y By Forward Euler…

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Q: Show that an implicit solution of 2x sin2(y) dx – (x² + 11) cos(y) dy = 0 is given by In(x² + 11) +…

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Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: What is the differential equation of the orthogonal trajectories of х3 — Зху — у3 — с? (1) (x +…

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Q: Show that the general solution of y(4) − y = 0 can be written as y=c1cost+c2sint+c3cosht+c4sinht.…

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

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A: 10 Given solution of differential equation is x(t)=c1cos ωt+c2 sinωt of the differential equation…

Q: What is the differential equation of the orthogonal trajectories of x3 = Cy? (1) Зxdx + 2уdy — 0 (2)…

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Q: 1. Solve for x(t) and y(t), given that x(0)=4 and y(0)=3 dy - y = 0 dx + x + 4y dt — 10%; х - | dt

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Q: dl ) Verify that y = C₁ cos(3x) + c₂sin(3x) is a solution of 2); A) (::. - y" +9y = 0 B) {….. y' +…

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Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) .  f"…

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Q: dy -y ze°Cos(E) dt y le) =0 1+らine

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Q: 5 By Separation of variables, Solve the following PDES :- ²4 J² ● dt² dx² 0 o u(e,t) = u(s, t) =6…

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Q: 36. Using the approximation dy dy h dr * Yn+1- y. and that dr 1, y = 2 when r 0. Then, y A h- 2 h+ 2…

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Q: we solve thd DE y dx 2x0y-0aer convedding it to oad sing an integrating tactor, then the solution…

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Q: If f(x, y) = 4x² – 6y², then the total differential of f at x = 1 and y = -2 is : O df = 24 dx + 8…

A: df=dx+dy (see step 2).

Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: 1. Solve the DE as follows: d'y dy +3- 2 dt +2y= 24 y(0) = 10 and y'(0) = 0 dt

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Q: 9. a) Apply fourth order Runge-Kutta method to dy 3x + y/2, y(0) = 1 dx to determine y(0.2) correct…

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Q: Find the generat Solution t dy (2y + xy) dx or Special o the differential * +1=

A: We have to find the general solution to the differential equation 2y+xydydx=1+4x+4x2

Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: Let y(t) be the solution of (x3 + 1) dy dt = y satisfying y(0) = 1. Compute approximations to…

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Q: 5 By separation of variables, Solve the followin PDES :- du dt d2u dx2 @ o U (0₂t) =(4,t) = G u(x,0)…

A: Given is the Partial Differential equation ∂u∂t=2∂2u∂x2…

Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: 6. Find the general solution to the DE. Show all of your work. dy =-0.2y+10 dt

A: Particular Differential Equation: A differential equation which is either in the form of , then the…

Q: What is the differential equation obtained by eliminating the parameter A from the relation y = A+…

A: In this question we need to find a derivative of the given equation.

Q: Find the solution of the differential equa­tion that satisfies the given boundary condition(s) . y"…

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Q: By direct partial integration, Solve the following PDES 8- 82u = COSX COSYSXUCX,t) Ex u(π, y) = 2…

A: Given ; del2u/delx del y=cosxcosy.

Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

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Q: 22) Use Euler method to estimate the solution of the ODE y' (xy?) ,y(1) = 2, h = 0.1 at x = 1.2

A: using the Euler's rule: yi+1=yi+hf(xi,yi) we will find the solution of given ODE we have…

Q: 4. An earth satellite moves in a path that can be described by x2 72.5 = 1 71.5 where x and y are in…

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Q: d*y 4)5t- dt + 3t () – (sin t)y = 0 dt 4 5)(sin x)y² + 2 y = 3x³ – 5 %3D 6) xy ? + 3 xy - 2 x³ y = 7

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: Let A and k be positive constants. What is a solution to dy/dt=k(1-Ay)

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Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: - Find where the 2 t r general Solution of 2t dy + 2y dt constant 2 dr ² is 6 Tr r t

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Q: Find dy/dt. 7) y= (ecos(u7)4 A) - esin(u7)3 B) co4 cos(/7) COS e3 cos(t/7) D) - sin e4 cos(t/7) Find…

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Q: с. (х — 2у)dx + (у — 2х) dy %3D 0

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Q: 5.Express this model of an electric circuit d²y dy +6 +5y = sin10t, y(0)=0, y'(0)=1 dt² dt As a pair…

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Q: ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0…

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Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: 4. Show that al f(t) sin a(r – t)dt Y solves the initial value problem dy +a?y = f(x), dx? dy = 0…

A: The given initial value problem is                   d2ydx2+a2y=f(x), dydx=0 and y=0 when x=0. We…

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

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