(b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

Q: 5. Solve the diffusion equation = v dt drr dr

A: ∂θ∂t=v∂2θ∂r2+1r∂θ∂r such that- r=0, θ is finite, t>0r=a, θ=0,         t>0 and θ=P4μa2-r2

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Q: 2) A: By using partial method solve [2x² cos x dx

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A: Given a nonlinear system, Let  fx1,x2,x3=x13+x12x2-x2x3+6gx1,x2,x3=ex1+ex2-x3hx1,x2,x3=x22-2x1x3-4…

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A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

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Q: Use Algorithm 12.1 to approximate the solution to the elliptic partial differential equa a?u a?u + =…

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Q: 2. Find the particular solution using the initial condition. ry'-y = x,y(1) = 7.

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Q: 5. Apply the Euler-Cauchy method with step length h to the problem y'=-y, y(0)=1 h = 0.1

A: y' = -y , y(0)=1 and h=0.1 f(x,y) = y' = -y  x0 = 0   and  y0 = 1

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Q: Apply Euler-Cauchy Runge-Kutta method for the equation: y' = 2y t y (1)=1 and and abtain y, Y₂ y h =…

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Q: Use Euler's method with step size h = 0.2 to approximate the solution to the initial value problem…

A: As per our guideline we are supposed to answer only first asked question.kindly repost other…

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Q: solve a initial value problem for Cauchy-Euler equation x^2y′′−3xy′+ 5y= 0, y(1) =−1, y′(1) = 4.

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Q: X' : 0 1 X + sec t tan t) -

A: Given

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.