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.(6š„2 āš¦+3)šš„+(3š¦2 āš„ā2)šš¦=0
X3+x2y-xy2+y3/x2y+xy2
whetther homogeneous or not by dx/dy
Solve the boundary value problem
y''-y=0
With boundary condition
y(0)=0, y(2)=3.6268
y''(x)+p(x)y'(x)+q(x)y(x)=r(x)
y'(0)=0
y(1)=a
Write the boundary condition in discretized form
True and False with explanation
1.Eqn y"-2xy'+xĀ²y=e^(xĀ²/2) and y"+y=1 have same normal form.
2.EquationĀ
cos(x+y)p +sin(x+y)q =zĀ²+z
is a quasi-linear equation.
3.Ā Every solution of the ordinary differential equationĀ (DĀ²+1)Ā²y=0 is bounded on
[0, infinity[.
4.For the IVP, dy/dx=f(x,y),y(x0)=y0 the continuity of f(x,y) and df/dx Guarantees unique solution of the problem
Do the functionsĀ
y1(t)=āt and y2(t)=1/t
form a fundamental set of solutions of theĀ
equation 2tĀ²y"+3ty'-y=0
, on the intervalĀ
0 < t <infinity
Justify your answer.
d^2y/dx^2 + 2dy/dx +5y=34sinxcosx
d2x/dt2=x-2y, d2y/dt2=4x+5y find general solution using matrix method.
Solve two dimensional Laplace equation dĀ²u/dxĀ²+dĀ²u/dyĀ²=0 ,subject to the condition u(0,y)=u(l,y)=u(x,0)=0, u(x,a)=sin nmx/l
yz(y+z)dx+xz(x+z)dy+xy(x+y)dz=0
