Use Euler's method to obtain a four-decimal approximation of the indicated value. Carry out the recursion of the equation Yn+1 = Yn + hf(xn¹ Yn) by hand, first using h = 0.1 and then using h = 0.05. y' = x + y², y(0) = 0; y(0.2) (h = 0.1) (h = 0.05) y(0.2) y(0.2)

Q: 2. Use Euler method to compute ys for the DE yy'=2x for y(1)=3

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Q: 3.2 Solve the following DE: (y + 4x) y' = 2y - x

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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: Solve the root of the equation y =7sin(x) e*- 1 using Bisection method with XL = 0 and XU = 0.5.…

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Q: Use Improved Euler's Method to approximate y(0.7) for y'-y²-1=0; y(0) =0 Use h=0.1. Calculate up to…

A: Using Improved Euler's Method , we have to approximatey(0.7)  for   y'- y2 -1 = 0 ,     y(0)=0Also…

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

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Q: Find 一 az ay -0 if z = (6x + 5y) 7.

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Q: Solve the ODE by the Euler method: given 2y" = -4y' - 1.5y y(0) = 3 and y'(0) = −2.5 with step h =…

A: To find- Solve the ODE by the Euler method: 2y'' = -4y' - 1.5y       giveny0 = 3 and y'0 = -2.5with…

Q: y" – 2y' + y = -3 –x+x, y(0) = -2, y(0) = 1.

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

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Q: (6xy + y² − ysin(xy))+(3x² + 2xy-xsin(xy))dy = 0

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Q: Find H(−2) and H'(−2), where H(x) =

A: Here we have;  H(x)=∫-2xduu2+1

Q: Solve this ODE by Heun's Method and h = 0.1 to find y(0.2) y' = -3x ,y(0) = 0 0.04 O 50 1 50 3 50 1.

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Q: 2ty t²+1 – 2t – (2 – In(t² + 1))y'

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Q: Approximate y(0.8) in the function y' = x - 2y when y(0) = 0, x(0) = 0 and the stepsize is 0.2 using…

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Q: Each of the following ODEs can be made variable separable using a substitution. Give the…

A: We have to find a suitable substitution and separate the variable for the differential equation

Q: By= In(Cx-2)

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Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: Runge-Kutta 4th

A: y' = y-x   , y(0) =2here h = 0.1f(x , y ) = y-xx0=0y0= 2y(0.1) = y(0) +16(k1+2k2+2k3+k4)k1 = (0.1)…

Q: Solve item 1 only. Find the general solution. Note: Use y" and y' as forms of terms, not dy and dx…

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Q: Use Newton's method to approximate a root of the equation In(5x) = arctan(x -0.1) as follows. Let x₁…

A: X

Q: Initially : 1/4 (j-10) = s+10 or s = 1/4j -12.5 Then 1/2 ( j-34) = s+34 sub in the equation above…

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Q: y'-2 xy=2 y (0)=1

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Q: Solve X' = AX: 1 1 1 A = 1 0 -1 1 3

A: Find the eigenvalues of A.

Q: dy Q4 Solve (1+ x)- xy = (1+ x)* e* .

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Q: Solve the 2nd order D.E. below using method of undetermined coefficients : y''+ 7 y' = 42 x^2 + 5x…

A: To find the solution, first, solve the homogenous ODE, y''+7y'=0 and obtain yh=C1+C2e-7x.…

Q: (3xy + y²) + (x² + xy)y' = 0.

A: Given differential equation: We have to solve the given differential equation.

Q: (2g (x) + 4) dæ = 22 and g (x) da = 12, then g (x) dæ 10 /3

A: Given; The integration of [2g(x)+4] limit from -1 to 3. And the integration of g(x) limit from 10 to…

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

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Q: 0 Suppose y' = = [-2₂ 3] x + [8] c y 3 et. Find yp.

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