What is the solution of given initial value problem? =y+ sin t dt2 d'y dx + cos t dt %3D dt2 (0) = 1, z'(0) = 0, y(0) = -1, y'(0) = -1 %3D %3D %3D O a. z(t) = cos t, y(t) = Cos t - sin t O b. z(t) = cos t, y(t) = - cost +sint %3D Oc. (t) = sin t, y(t) cos t + sin t %3D %3D O d. z(t) = cos = cos t, y(t) = - cost- sin t | %3D O e. r(t) = sin t, y(t) = -cost – sin t %3D

Q: What is the solution of given initial value problem? =y+sin t df2 da + cost dt de * (0) = 1, a' (0)…

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Q: d²x dx 2 + 10x = e2t x(0) = 0, x'(0) = 1 %3D - dt2 dt

A: Given differential equation is d2xdt2−2dxdt+10x=e2t. and x0=0, x'0=1 Write the auxiliary equation…

Q: (a) Differentiate: (i) 7x2 + 14 (ii) e*(4x² + 3)

A: Since you have posted a multiple question according to guildlines I will solve first question(Q.a)…

Q: d'y dy -4- 4- dx? dx -3y=0. y(0)=1, y(0)=5

A: According to the given information, it is required to solve the given differential equation.

Q: dy x COSY dx - siny=0 6 xcos)

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Q: dy/dt^2 – 4dy/dt – 5y =0, y(1) =0 ; y’(1) =2

A: Given differential equation d2ydt2-4dydt-5y=0  , y(1)=0 and y'(1)=2

Q: d sin x 1 dt| = dx et + 5 cO X 1 1 1 (A) esinx + 5 (B) e* + 5 (C) (esinx + 5) cos x (D) e sin x

A: We know that integration power rule is given as - Integration of xn is nxn-1.   Here i attached the…

Q: Solve dy (a) dx dy 1+y (b) dx 2x y+1 dy (c) (1+x 2+x dy (d) e*+y

A: Since you have posted a question with multiple sub-parts, we will solve the first three subparts for…

Q: 25 x²y dx = (x³ – y³) dy; y(1) = 1 |

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Q: xy' + y = 0, y(4) = 6 %3D

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Q: y" + 6y' + 8y = e-³te5t, y(0) = 0, y'(0) = 0 a. (e³t-1)²e-5t 3 b. (et - 1)³e5t a C. (et - 1)³e-5t 3…

A: The given initial value problem,.We have to find the solution to the IVP.

Q: y-HY + 3Y=0

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Q: Determine the value of dy/dt at x = 2 when 3x² - 5x and dr/dt = 2. y = 1. 2. 3. dy dtx=2 dy dt=2 4.…

A: The given function y=3x2-5x. We have to find the value of dydt at x=2 and dxdt=2.

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

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Q: #cost+y)+tanh' (sint) = In 3+ yuech (+)

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Q: Solve for x and y where dx/dt = x^2 + xy, dy/dt = y^2 + xy subject to condition x = 1, y = 2 at t =…

A: Non linear system of differential equations

Q: (c) y = 2 (f) y = sin ¹ r (i) y = x ¹⁰ 10

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Q: Solve dy dx Option 1 - y tan x = -y² secx 1- y = sec² x + tan x + C 3- y = secx + tan² x + C 2 y-¹…

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Q: (a) y = Vtan(7.r5 + 5 cos(5x)) %3D

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Q: d’y_2dy 3 y=2sin°(x) dx Determine the general solution of 2 dx

A: We have to determine the general solution of the differential equation…

Q: 4. (sin y - y sin x) dx + (cos x +x cos y- y) dy = 0

A: Note: As per our guidelines we are allowed to solve one question

Q: dy = 1+y² dx y' = yx³

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Q: Find dy dx || dy dx x2 2 x2 for y=x | tant d dt 2 dt + (Type ex

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Q: ntegration of dx/dt=x+2t ? Please explain it.

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Q: Solve ởy ôt y (x, 0)= 3 sin 2n x, y (0, t) = 0 = y (1, t); 0 0. %3D ốt

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Q: Y= (X+SinCe)? Find a(x) and fG) y=foq> (x) 3. (fog)'= %3D X+Sin(x) gcx) at y ' ( x)) X+ Sin (x. %3D…

A: (fog)(x)= f(g(x)) So, f is the outer function and g(x) is the inner function.

Q: Calculate S (xyz) dz dy dx. (x=1 cy=1-x cz=2-x x=0 Jy=0 Jz=0

A: Solution-

Q: 음(sinh-1(x)) = EXAMPLE 4 Prove that + x2 SOLUTION Let y = sinh-(x). Then sinh(y) = x. If we…

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Q: ans 늘 sin ()+c 19 -4x² teinx dx I+ x2 dx ans: į sini'Ln'xte 3. sečxdx ensesin 3tanx 15-9tañx dx

A: Since, you have posted multiple questions. As per guidelines, we"ll solve only first question. If…

Q: Find dy/dx if y=- O dy dx Ody dx O dy dx O dy dx = = = 1-t 1+t = sec 2t (1+t) ² (1+1) 2 sin2t cos2t…

A: To find dydx if y=1-t1+t and  x=cos2t.

Q: Зх- 1 | (*-9) dt Use Leibniz's rule to find for y = dx

A: Leibniz's Rule:ddx∫a(x)b(x)f(x,t)dt = f(x,b(x))·db(x)dx +  f(x,a(x))·da(x)dx - ∫a(x)b(x)∂f(x,t)∂xdt…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.