Use a substitution of the form y = (x − c)' to find a general solution to the given equation for x> c. 3(x − 5)² y''(x) + 13(x − 5)y'(x) − 8y(x) = 0 BELED

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Q: Let α(x) = ex2 . Verify the identity (α(x)y)' = α(x)(y' + 2xy) and explain how it is used to find…

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Q: I Solve the differential equatons when X= (x+y) dx +(2xy+xh 3x) dy=o 1. Y= 2

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Q: Use the method of undetermined coefficients to solve the ODEy′′ − 3y′ + 2y = e^x

A: We solve the second-order non-homogeneous ordinary differential equation (ODE):y′′−3y′+2y=exusing…

Q: n of (3x²–

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Q: (D²1)y = 5 sin² x ; y(0) = 2; y'(0) = -4

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Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: -3/2 -¹² (2²³ + 2x) da with y(0) = 0, y(3/2) = 1. (c) J[y] = =

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Q: y′ = −y(5 − y)

A: Recall the following fact.

Q: 1. ƒ(x)=x²- = x² - secx 2. w = ex²-x² + 4x 3. h(z)=In(2z)sin(2z) 3x² 4. y= √x² +1 5. y³ + 2xy = 3

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Q: Use the method of undetermined coefficients to find the solution to y''+y=4x+10sin(x) that is…

A: Method of undetermined co-efficient: For given a non- homogeneous ODE of the form…

Q: Find the differential of the following function: a) f(x) = x (2x³ + 9x)5 2t b) f(t) = (₁²₂)4 1-t2

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Q: Solve (1-x)y'(x) + xy(x) =ax O a. y(x) = a+ k(x? -1) O b. y(x) = a+kVI-x %3D O. C. y(x) = a + kyx?…

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Q: 3. Show that the equation (6ry – y*)dx + (4y + 3x² – 3xy²)dy = 0 is exact. Hence solve the equation…

A: Solution:

Q: у y = '2 when x = Га 0= x phx + hp (hq - zx) X

A: Compare this equation with,So here we have

Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

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Q: Classify each of the equations above as autonomous, separable, linear, homogeneous, exact,…

A: I am solving questions ( B I and J ) as per the guidelines we can solve max 3 sub part of a question…

Q: Given that y(x)= sin( In 2x ). Which of the following formula is CORRECT to find y'(x). v(e) = (In…

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Q: In general, solving y' = 0 leads to Select an answer .2 Now, let y = f(x) 9 In(æ|). Determine y'. 2…

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Q: z = xy dy x2+y= 2x/1-x’y² dx 2. Using the substitution ,change the to a separable equation. Hence…

A: We are given the differential equation  xdydx+y=2x1-x2y2 we have to use the substitution z=xy.

Q: Using Improved Euler's method, Solve for y(1.5). y' = (1-x-1)y y(1) = 1 h = 0.1

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Q: Solve by variation of parameters method (h) y" + y' = tan x

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Q: 8. (y2 + 7xy + 16x²)dx + x²dy = 0,when x = 1, y = 1

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Q: For an arbitrary constant c find a particular solution to y'' − y = e^cx

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Q: Find the solution of xy" + 5xy +(4 – Ix)y = 0, x > 0 of the form where co = 1. Enter n= 1,2,3, ...

A: Let the solution of the above differential equation is given as: y=xr∑n=0∞cnxny=∑n=0∞cnxr+nThe…

Q: Determine the solutions of the equation valid near the origin for x>0? 2xy''+6y'+y=0

A: Given differential equation is 2xy''+6y'+y=0               (1) Comparing with y''+Py'+Qy=0 Here…

Q: (b) Use the substitution u = x In y to solve the equation (xy + 2ry ln² y + yIn y)dr + (2x² In y…

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Q: [Q3] Using the method of undetermined coefficients. (a) Solve y" - 2 y' - 3 y = 2e* -10 sin x, y(0)…

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Q: Find for x = 1, the value of the particular solution y of the following ODE: 4 y"-4y'-3 y=0,…

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Q: z(x) 1+x² You need to find the formula for y'(x) first, then evaluate y'(x) at x = (c) Let y(x) = =…

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Q: 5. Exact Diffe re ntial Equation: x(3xy – 4y' +6}dx+(x' – 6x² y² -1dy =0

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Q: Find the general solution of the following equation.Primes denote derivatives with respect to x.…

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