Q1) Solve the following system of algebraic equations using matrix inverse method. 6 30-0 Q2/ Solve the following differential equations. 1) + y² - 4: 2) 1/4+3/4+2y=0 Q3/ Find points of intersection for the following curves. 1- r = 1+ cos 0, 2- r = 1 + sin 0.

Q: Find the solution of the given ODE a. 1 - 2 = Cx b. 1 + (-)² = Cx c. 1 - * = Cx y d. 1 + (-)² = Cx…

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Q: 5) y' = 2л —2у+1 X-Y

A: As you asked multiple questions , I only solved the first one.

Q: valuate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1…

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Q: 5) Given the following differential equations with output x and input y, linearize the equations…

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Q: Match the general solutions to the differential equations. (D²+20+5)²y=0 ✓(D²-6D+10)²y=0…

A: The given differential equations, D2+2D+52y=0D2-6D+102y=0D2-8D+252y=0D2-4D+292y=0 We have to find…

Q: Let A = a. Find A 1 2 5 12 = G] 5 19 b3 - 2 - 16 4 +-[12] and b4 1 and use it solve the four…

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Q: d) ху" +2(x-1) ц' -Gy=x4+2/sx-4c-x

A: Given differential equation:To find:The solution to the second order non-homogeneous differential…

Q: Four differential equations and four functions are given below. Each function is a solution of one…

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Q: Solve the Euler- Cauchy equation

A: We solve the given differential equation using Euler cauchy method.

Q: Express the system of differential equations in matrix notation. x' = (e ¹)x+ (at + bt³)y y' = (tan…

A: The given system of equations is ,           x' = (et)x + (at+bt3)y             y' = (tan t)x + (…

Q: Use the method of undetermined coefficients or the method of differential operators to find one…

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Q: Solve the following equations by Ferobenius' method: x(x-1)y +(3x-1)y'+y=0 x²y-5xy'+9y=0 x²y+6xy'…

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Q: [y(4)]² + 4 y™ + 3 y² + 2y² = cos3x 2y¹ + (y)¹/3 + 3y = √5 O y + 4y" + 5y = lny"

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Q: Find the general solution to the simultaneous system of differential equations and its intervalof…

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Q: Calculate the general solution for the homogeneous system of first-order equations. y₁ =6y₁ + y₂ y₂…

A: [Note : As per the guidelines I am answering only one question at a time]Given differential…

Q: If e* and xex are solutions of y"tay'tby=- Are soluhons linearly independent? write the soluhion.…

A: Given that e−x and xe−x are the solutions of y''+ay'+by=0. We have to check whether the e−x and xe−x…

Q: X= [+] -3 1 X × ² = [ 2² -4 ] X X2-26-561 est

A: For the differential equation, to checkand the set is fundamental set of solution.

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: differential equation. neral solution of the giver ation, if e and ex are E 5u -

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Q: M₁=0.0.85.fc'.a.b. d-- 5.fc²·a·b (d-a) 2 0-(480-) 2 200.106 = 0.9.0.85-20.7.a.300 480-

A: Sol:- Let f(a)=0.9⋅0.85⋅20.7⋅a⋅300(480-a2)-200⋅106Here f(97)=-1159168.925<0 and…

Q: x' = 4x + y + 2t, y' = −2x + y

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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: Determine the form of the general solution to the following differential equations с. у) + 5у2) —36у…

A: To solve given differential equation we used the method of undetermined coefficient. First we write…