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Write a program to solve and plot the solution of PDE

(D2 + 3D + 2 )z =0


Program-


/* program to find the solution of second order partial differential equation*/

F(D,D1)*z=0;

F(D,D1):=D

Write a program to solve and plot the solution of differential equation

 dy/dx=-(x²-y)/y-x at initial condition y(1) = 2


Program-2

/* program to solve and plot the solution of exact differential equation*/

kill(all);

eq:'diff(y,x)=-(x²-y)/(y²-x);

gsol:ode2(eq,y,x);

psol:ic1(gsol,x=1,y=2);

us:rhs(psol);

plot2d(us,[x,-5,5],[y,-5,5]);

Write the Output obtained by execution:


Solve the problem :
(1/(1+x^2) + cos t -2xt) dx/dt = x(x+sin t), x(0)=1
solve the problem d^2x/dt^2 +x=8cos2t-4sint, x(π/2)=-1, x'(π/2)=0
solve the problem d^2x/dt^2 +x=8cos2t-4sint x(π/2)=-1 (π/2)=0

 Find Z[n(n – 1) (n – 2)].


Solve the given problem by means of an eigenfunction expansion.

y"+2y= −x, y(0)=0, y'(1)=0


The velocity distribution in a two dimensional steady flow field is xy plan is v=(Ax-B)i+(C-Ay)j,A=2s-1,B=5ms-1,C=3ms-1. The coordinates are measured in meters and body force distributing is gx=-gk.Does the velocity field represent an incompressible fluid?Find the stagnation point of the flow field. Obtain expression for the pressures gradient in the flow field. Evaluate the difference at(x,y)=(1,3) and origin if density is 1.2kg/m3

  1. dy/dx - 2(x+1)³ = 4/(x×1) y adalah y = (x+1)⁴ In (x+1)²,diberikan x = 0 ketika y =0
  2. 2y(1-x)+x(1+y)dy/dx=0 dimana x=1 ketika y=1

A string is stretched and fixed between two points (0,0) and (l,0). Motion is initiated by displacing the string in the form ( ) and released from rest at time t=o. Find the displacement of any point on the string at any time t.