Solve the equation dy = X t y =4. X. C Hint : let V= ), the solution of it includes a constant C) using the initial condition to determine the value of C. Cnote: can determine the constant c you even be fore simplifying the general solution.)

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A: →∫1a2 + x2dx  = 1atan-1xa→ddxuv = udvdx + vdudx

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Q: Q4: Solve by using Separation of variables method? = 4 for 0 0 (0.e)=27.t) = 0 for t 20, u(x.0) =…

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Q: Use Euler's method to solve the following initial value problem. dy dy (x2 + 1) + - y = 0: = 0 and y…

A: x2+1d2ydx2+x dydx-y=0dydx=0,  y=0,  x=0      h=0.5Let  y1=y,  y2=y1'  x2+1 y2'+x y2-y1=0  y1'=y2…

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Q: 4(a)Verify that the equation y = Inx – Iny is an implicit solution of the TVP, ydx = x(y+ 1)dy y(e)…

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Q: Verify that y(x) = erx, with r satisfying ar+b = 0 is a solution of the equation ay' + by=0.

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Q: 8. Use variation of parameters. а. (D? — 1)у %3D ех + 1 Show Complete Solution Answers: a. y = c,e*…

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A: The given differential equation is: ty'=y+3y2+t2  ;       y(-e)=0