Find the general solution to dr tIn(t) +r = 6te". dt Enter your answer as r . ...

Q: Q1: Solve the following O.D.E у"- Зу'- 4у%3DЗе + 2 sin x - 8e* cos 2.x.

A: Note: We'll answer the first question since the exact one wasn't specified. Please submit a new…

Q: 3 de + 4 €²x³² + = ²0 dt

A: The given differential equation is ,                 dxdt+4x5t3 + xt = 0 (.)  Bernoulli equation :…

Q: x/3 Assuming i= and t is a real number. ſ "dt is A. 1 +i- 2 B. 1 2 2 D. 1+ 2 +i A O C D O C.

A: Given integration is : ∫0π3eitdt To find the value of integration.

Q: Show that 1/2 ( Tn + Mn ) = T 2n

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Q: (2xy tx?+x*) dx - (Itx²) dy=D0

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Q: ex solve the Disserentail eg using Exact method ylny dx +(1+x²) dy

A: We have to solve the given differencial equation.

Q: B. Show that f(x) = 2(In x)³ is a 3f(x) solution xlnx to the equation f'(x) = =

A: We have to show that y=2(ln(x))3 is a solution of given equation.

Q: Evaluate the following: a. [₁₂ (6 + e ²¹) 8(t - 4) dt = [ b. ₁ (6 + e ²¹) 5(t− 8) dt = [ c. L₁ (6 +…

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Q: 1. (x + √y² + 1) dx · (y – H.W. solve the following D.E. xy - - √12241) dy = 0

A: Step 1:

Q: 1 If = 1/2 = = a + b and ¹ = a - b, then x - y is equal to: x y

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Q: Solve the following DE x y" – 4y' = x e"

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Q: Which of the following functions are solutions of the DE y-4ry 0? (a) y 5z2 (b) y= e2 (c) y=3e1 (d)…

A: The given differential equation is Compare the above DE by general form of linear DE such that

Q: How do I solve T=I/PR X 360 for "R"?

A: The given equation is

Q: L[cost H(t- 7)] = %3D O A. s +1 O B. -1 e 3-1 OC. -1 -AS e * +1 O D. -S e 3-1 O E. e +1 2

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Q: Solve the following DE using the Method of Variation of Parameters y" + 4y = 4sec²2x

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Q: Find dt OA. ○ B. OC. O D. for y = (5t? - 4t)?. dt dy dt dy dt dy dt = 2 (5t² − 4t) + (10t − 4) =…

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Q: 1 x (1-x)ªdx= 1 105 a O 1 .b O 280 1 .cO 35 1 .d 210

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Q: Į va | Vi(t? + 6t +7) dt. 4. Find

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Q: 18) h(t) = 2 · 3**³; Find h(4 + t)

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Q: 1. e-st cosh t dt 2x +4 2. 2x2 + 21x + 34

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Q: 2. Solve the following: dt x> 2 X-y t+

A: The formula for the substitution method for definite integrals is given by , where g'(x) and f(x)…

Q: Solve the following: cInc y(1+V3+y2)y' with y(1) = -1. Do not solve explicitly for y. That is, you…

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Q: C = 2rr. Find C'. C' :

A: The circumference of circle is C=2πr where r is radius of circle. Here, r is a variable.

Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: z = xy dy x + y = 2x/1-x²y² 2. Using the substitution change the "dx to a separable equation. Hence…

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Q: dy Find the solution of the Bernoulli's equation x + 6y = 3xy4/3. dx 1 1 а. у b. y (x2+cx)3 (x+c)3 1…

A: We solve by Bernoulli's equation.

Q: A. 8-24x C. Find the second В. 8х + 10-6х-4 8+ 24x−1 8+24x-5 D c. Y = 4x² + 10x + -5 Find derivative…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 3. Find dy of the following equations: dx a. y = |(e-3x² + 7x² + In 8x

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Q: 1. Solve for the variable x. F = kx – kxo A. x=F-kxg А. х- O B. x=F-kx, k F- Kxo О с.х3 C. x= D.…

A: The given equation is F=kx-kx0

Q: Q6. Find general solution of the DE 4x²y" + 8ry' + y = 0

A: We need to find the general solution of the given differential equation. The general solution of the…

Q: - ydx + (x ++xy )dy= 0

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Q: Find the general solution of the following DE in explicit form. y' = 4+2/y -4x +5

A: To find: The general solution of y'=4+2y-4x+5. Concept used: Power rule of differentiation:…

Q: Find y/p(t), a particular solution of the equation V"-4y + 4y 3e2 ● t> 0.

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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.