Q1/ Use Elzaki Adomian decomposition method to solve the following nonlinear partial differential equations: 3 Pt+44x44xxx + 4xxxxx = 0, 4(x, 0) = ex Q2/ Solve the differential equation by Elzaki transform 3 y"-3y' + 2y = 4e3t, y(0) = -3, y'(0) = 5. Q3/ Find the approximate solution of the nonlinear partial differential equation == Uet - Uxx + u² = x+t+2x²-2t2, u(x, 0) = 0, u(x, 0) = 0

solve the first order differential equation with homogenous coefficients   consider M(x,y) dx + N(x,y) dy =0 if m is simpler, x=vy dx=vdy + ydv if n is simpler, y=vx dy=vdx+xdv   1.) (xy^2 - 4x) dx + (2x^2  +8) dy = 0 show your complete solution

By using separation of variables u(x, t) = X (x)T(t), break the partial differ- ential equation ди + u = 4 into two ordinary differential equations. Your answer may contain some constant ).

Obtain the differential equation of all straight lines at a fixed distance p from the origin * O (xy-y)*2=p[1-(v)*2] O (xy'+y)*2=[1+()^21 O (xy-y)*2=p[1+(y)*2] O cxy'+y)^2=[1+yl

Euler's method is a numerical method for generating a table of values (xi, yi) that approximate thesolution of the differential equation y' = f(x,y) with boundary condition y(xo) = yo. The first entry in thetable is the starting point (xo , yo.). Given the entry (xi , yi ), then entry (xi+1 , yi+1) is obtained using theformula xi+1 = xi + x and yi+1 = yi + xf(xi , yi ). Where h is the small value called step size.Use Euler's method to estimate the value of y when x = 2.5 for the solution of the differential equationy' = x + 3y/x with the boundary condition y(1) = 1. Take x = 0.1, the exact solution of this differentialequation is y = 2x3- x2. Compare your approximation values with the exact value