(xiv) f(t) = 3+et – te-2t + e5t cos3t + 6sinh7t

Q: 1 Laplace transforms Calculate the Laplace transforms of (i) H₂(t) cosh (3t), where cosh (at) = 1/²…

A: Solution: (i) let, f(t) = H2(t)cosh(3t)                   = H2(t)[(1/2)(e3t + e-3t)]…

Q: (11) Evaluate [[3x+5y+i(x²-y') dz along y=x (0,0)

A:

Q: Step 4 Finally, determine(-3x + 7) and (x + 7) and simplify the result. dx dx 1. du 1 dv + U dx V dx…

A: formulas we use: ddxf+g=dfdx+dgdxddxkx=k; k is a constant.dkdx=0; k is constant.ddx(x)=1.

Q: 2y′ + y = 3t2

A:

Q: L(cos3t) = S .a O s²+9 S .b O s+9 s2 –9 3 s2+9

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Q: 1. Find 2(3z + 4)² dz.

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Q: (2t+1)(2t-1) dt. 4. S

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Q: Ssin(2x+3)dx= d -1 cos(2.x+ 3)+C 2 a 5 cos(2.x + 3)+C -1 cos(2x+3)+C - cos(2x+3)+ C e cos(2x +3)+ C

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Q: + y²(x+ 1)² = C

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Q: x² + 4y² = C(x+y)

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Q: Find (e3x + 5sinx)dx. -e3x +5cosx +C O a. 3 e3x+1 -5cosx + C b. 3x + 1 e3x -5 cosx + C OC. -e3x -…

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Q: 1 1-¹ ( ( 5 + + 2) ³) 3 = Find ac + b. α ~tbeat C

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Q: Compute dx. X + 2 *+ C Ox-2in|x| +C + C 2+ 2x Ox-2injx + 21 + C + C (x + 2)2

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Q: The tanh (2x) sech (2x) dx is equal to sech (2x) sech (2x) +C OA 3 10 OB. sech (2x) sech (2x) +C. 3…

A: Solution

Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the general solution: (x² D² + 6xD+6I)y= x²?. Select one: O a. y = 20 0 -3x O b. y = (c1 +…

A:

Q: [ arctan (1-x)]² 4x2- 8x+8

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: a va?-x? a²-x² (x + y) dydx

A: We have to find the value of given intregation.

Q: Find the complete solution of the DE (D3+6D2+11D+6)y=ex +cosx.

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Q: 6х —9 4.) dx 22— 3х +2

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Q: Solve (e²y - y) cosx = e sin2x dy dx Select one: O a ev + 2yev-e2cosx = c O b. e+ ye+e-2cosx = c Oce…

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Q: 4.a) Find d dx y = ln (2²/ n (²x + 5) b) Find dy dx y = 3√√x++2x e³x (5x²)

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Q: 9 = dy

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Q: Find the general solution of y" - 6y"=3 - cosx.

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Q: . Solve the first order equation (3z²y + 2ry)dx + (x³ + x² + 2y)dy = 0.

A: Solution

Q: Find // (4x + 2y)dA where D = {(x, y) | a² + y? 0}

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Q: 2. 2 cos(3r) dr

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Q: 3n 2n n S " S"(sin x + cos y)e? dx dy dz 2n 'n A. 2n(e2n + e3™) в. 2п(е2т — езт) c. 2n(e3™ + e2") D.…

A: Given: I=∫2π3π∫π2π∫0πsinx+cosyezdxdydz   We know that; ∫sinxdx=-cosx+C∫cosxdx=sinx+C∫exdx=ex+C And…

Q: cos(3w) (iv) 1+w2

A:

Q: Solve the following DE: (x² + 2xy-4y²) dx - (x²-8xy-4y2) dy=0 Ox²+4y²=C(x+y) Ox²+2y²=C(x+y) O x² +…

A: Given DE is x2+2xy-4y2dx-x2-8xy-4y2dy=0 The solution is determined as shown below.

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.