of y'(x) -ay(x) = 0   (see answer in picture) Task: use the above

Q: y"+y' - 2y = x2

A: Solution :-

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

A:

Q: Find the general solution to y''-1=0

A: y''-1 =0y'' = 1y' = ∫1 dxy' = x + By =∫(x + B) dxy = x22 + Bx + A

Q: (c) xy" + y = 36x

A:

Q: 4. (6 points) Using separation of variables, solve the differ- ential equation, (1+7)dy dx y Use C…

A:

Q: The green graph below shows the graph of the solution to 1 29 +by' + cy=0 y(0) = 0, y'(0) = 1 for…

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Q: y y' + y? = x-2 X

A:

Q: Solve the equation y" – 10y' + 25y = t-5e5t.

A:

Q: p" +2y' – xy = 0 n(x)= e

A: Given

Q: 2. ye*dx + e*dy = 0

A:

Q: How do I find the particular solution yp in the equation above?

A: For particular equation we will crate function for particular integral. Then we solve it by using…

Q: Find the general solution to y'" + y = 0 Show the solution.

A:

Q: B. ty" – (t+ 1)y' + y = t?

A: Answer is mentioned below

Q: Equation: Answer:

A: We want to find value of x. For this we use Pythagoras theorem, which states that Hypotenuse2 =…

Q: Euler Equation: t2y''+ty'+y=0, t>0

A: Here I am attaching image so that you understand each and every step.

Q: Solve by undetermined coefficients. y" – 3y' = 6e – 2e", y(0) = 0, y (0) = 0.

A:

Q: Find the general solution of the equation y" – 2y' + 5y F0 Do not need to show your work, just give…

A: First we find the auxiliary equation and then we find the general solution of the given homogeneous…

Q: Verify that the function y = c1e (-k+2t)x + c2e (-k-2t)x is a solution to y " + 2ky'+ (k 2 + 4)y =…

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Q: ) Verify that y=e-2x is a solution of equation x(y")3+ (y')4 – y = 0

A:

Q: 1. Write the equation in the standard form. (2) (1-2x-x²)+2(1+x)y'-2y=0

A: The standard form of the second order differential equation is: y''+P(x)y'+Q(x)y=f(x)

Q: Ex. (9) Sol:- Solve 3y"-2y'+y= 4x+2

A:

Q: Is (y − 33)2 = 4a(x − h) the solution to the diff. equation (y-33)y''+(y')2 =0

A: soln:Giveny-332=4ax-hdifferential equationy-33y''+y'2=0

Q: Find the general solution of the equation y" – 2y' + y= 0 Do not need to słow your work, just give…

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Q: Find the general solution for y"" + 2y" + 2y' = 0

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Q: Evaluate the general solution of y""=e4x + sinx

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Q: Find the general solution for the following equation: y' = (2²4) (3y + 2)

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Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Solve: y' + 4y - 17y' - 60y: = y(0) = - 4, y'(0) = - -5, y(t) = = - 72et y''(0) = - 65

A: First we will find the Auxiliary equation of given differential equation to get Complementry…

Q: Find the general solution of the following equation valid near the origin: (1+4x2)y''-8y=0

A: