Solve your IGNOU Doubts

Question:

Find the deflection of the fixed end vibrating string of unit length corresponding to zero initial deflection and ) u(x given below as the initial velocity.

$u(x)=\begin{cases}x,&0\le x<\frac{1}{2}\\1-x,&\frac{1}{2}\le x<1\end{cases}$

See Answer →

Question:

Find the directional derivatives of f(x, y, z) = x² + 2y² +3z² at P_o (1, 1, 1) in the direction of a =i+j+k

See Answer →

Question:

Solve the differential equation

$p^2+2py\cot x-y^2=0$ where $p=\frac{dy}{dx}.$

See Answer →

Question:

Find the complete integral of p² +q²-2px-2qy+1 = 0

See Answer →

Question:

Find the integral surface of the linear p.d.e. x(y² + z)p-y(x² + z)q = (x²- y²) z which contains the straight line x + y = 0, z = 1

See Answer →

Question:

Find the differential equation of the family of surfaces $\phi(x+y+z,x^2+y^2-z^2)=0$ What is the order of this p.d.e?

See Answer →

Question:

Verify that the equation

$2(y+z)dx-(x+z)dy+(2y-x+z)dz=0$

is integrable and find its primitive.

See Answer →

Question:

Solve: $(1+x)^2\frac{d^2y}{dx^2}+(1+x)\frac{dy}{dx}+y=4\cos\ln(1+x)$

See Answer →

Question:

Solve the IVP : $x^2\frac{dy}{dx}=\cos x-2xy,\quad y(\pi)=0,\quad x>0.$

See Answer →

Question:

Solve : $\frac{d^2y}{dx^2}-4x\frac{dy}{dx}+(4x^2-1)y=-3e^{x^2}\sin 2x.$

See Answer →

Question:

Solve the PDE

$x^2\frac{\partial^2 z}{\partial x^2}-y^2\frac{\partial^2 z}{\partial y^2}+x\frac{\partial z}{\partial x}-y\frac{\partial z}{\partial y}=\ln x$

See Answer →

Question:

Solve the following boundary value problem

$u_t=u_{xx},\quad 0<x<l,\quad t>0$

$u(0,t)=u(l,t)=0$

$u(x,0)=x(l-x),\quad 0\le x\le l$

See Answer →

Question:

Find the general solution of the differential equation $\frac{y^2}{2}+2ye^t+(y+e^t)\frac{dy}{dt}=0$

See Answer →

Question:

Find the orthogonal trajectories of the family of parabolas x = cy² and sketch their graph.

See Answer →

Question:

if y₁ = 2x + 2 and y₂ = -x²/2 are the solutions of the equation y = xy' + (y')²/2 then are the constant multiples c₁y₁, and c₂y₂, where c₁ and c₂ are arbitrary, also the solutions of the given DE? Is the sum y₁ + y₂ a solution? Justify your answer.

See Answer →

Question:

Solve the following differential equations:

i) $\frac{dx}{y^2(x-y)}=\frac{dy}{x^2(x-y)}=\frac{dz}{z(x^2+y^2)}$

ii) $(yz+z^2)dx-xzdy+xydz=0$

iii) $(z+z^3)\cos x\,dx-(z+z^3)dy+(1-z^2)(y-\sin x)dz=0.$

See Answer →

Question:

If ƒ and g are arbitrary functions of their respective arguments, show that $u=f(x-vt+i\alpha y)+g(x-vt+i\alpha y),$ is a solution of $\frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\partial y^2}=\frac{1}{c^2}\frac{\partial^2 u}{\partial t^2}$ where, $\alpha^2=1-\frac{v^2}{c^2}.$