Suppose ay" + by' + cy = 0 with y(0) = d and y'(0) = k has a general solution y = 4e2 3. What are the constants a, b, c, d, and k?

Q: Solve the following second-order equation  xy'' + 2y' = 24x2  by making the substitution u = y'.   I…

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Q: show that y=x2 is one of this equation solutions x2y''-2y=0

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Q: Find a real general solution 5x^2 y"+23xy′+16.2y=0

A: Consider y=xm and solve using this substitution to obtain the required general solution.

Q: Solve the equation y''' - y'' - 2y'= 0

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Q: Find the general solution by undetermined coefficients.  y'' + y = 2x2e-x.

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Q: Find a particular solution to the given higher-order equation. y'"' - y'' - 22y' +40y = - 40t²…

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Q: Show that y = 5x2 + 2 is a solution to the DE xy' +(2)/(5) y" = 2y.

A: To show: y=5 x2+2 is a solution of differential equation xy'+25y''=2y

Q: y"" + 3y'' − 4y = 0. Find y . Please check the equation carefully and then start

A: We have given equation y''''+3y''-4y=0   Auxiliary equation of differential equation is  m4+3m2-4=0…

Q: Suppose ay″+by′+cy=0 with y(0)=d and y′(0)=k has a general solution y=5e^(3x)−xe^(3x).   What are…

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Q: Find a real general solution x2y"+0.7xy′−0.1y=0

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Q: Suppose A is changed to A' .How large a relative change can this change produce in the solution to…

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Q: e a. y; = +e-2= In(e" +1) +e-* In(e" + 1) – 6 2 b. Y, = re2" + e In(1 + e") – e2" In(1+ e") C. Y; =…

A: Option (a) is correct.   See the solution in the attachment.

Q: Solve for y in two ways. y' - 5y = -3

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Q: How do I solve for the third order y''' - 4y''-11y' + 30y = 4e^8t + t^2 using the method of…

A: For the given third order differential equation we need to determine the general solution which is…

Q: bx2 ) e x2c +d X. dx

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Q: Find a particular solution y'''-y''-4y'+8y=6xe^2x

A: y'''-y''-4y'+8y=6xe^2x Particular integral = 6xe2x 6xe2xD3-D2-4D+8By using property shift F(D) to…

Q: Find a particular solution to y" + 5y + 4y = -10te". Yp =

A: Given the D.E. y''+5y'+4y = -10te3t We have to find particular solution yp of this equation.

Q: Solve for ‘x’ and ‘y’ where x + y = a – b, ax – by = a2 + b2

A: To solve the equation for x and y.

Q: Find the general solution to (t² + 4)y' + 2ty = t²(t² + 4). Enter your answer as y = .... Use C to…

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Q: Solve for Y(s) and Y(t)

A: Y(s)=s4−10s3+61s2−360s+9006s3−55s2+217s−1986​ (PLEASE SEE DETAILED INFORMATION ON THE EXPLANATION…

Q: -4 -3 2 -1 -1 4 -2. -3+ y = x2 - 4 A y = x2 - 4x y = x'- 4 y = 23 4x - ©2021 Illuminate Education…

A: our answer is y=x3-4x

Q: If ty'+y=6, y(1)=3 , what is the solution to the equation?

A: Consider the initial value problem: ty'+y=6, y(1)=3. Rewrite the equation:…

Q: In Calculus you will see the symbol y'. Treat y' as a variable and solve the equation for y. 6y²y +…

A: To solve the following equation for y'. 6y2y'+30xy+6x2y'=5y2+25xyy'

Q: Find y'' for y = 5x +4. 25x2 y'= - O A. 2 (5x? +4) 1 y" = O B. 4 (5x2 + 4) 20 y" = OC. (5x? + 4)…

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Q: What is the special solution of the equation y0̅ ? y''' + 5y'' + 12y' + 8y =5sin2x +10x2 - 3x + 7

A: Find the attachment

Q: A virus is believed to be spreading through a sheep farm according to that equation N = 450 (11 +…

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Q: 8 If x2 = 25 - y2, what is the value of dx2 a²y at the point (3, 4)? 25 (A) - 64 (B) - (C) (D) (E)…

A: use the quotient rule to find the second derivative.

Q: Which of the following is the solution to the equation shown below in terms of the constants a, b,…

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Q: How to solve for the equation y''' + 4y'' + 5y' + 2y = 4x + 16 using Undetermined Coefficient…

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Q: Find general solution y = Yc + Yp of y(3) + y" 3e" + 4x2

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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.